## Waltman, Paul Elvis

Compute Distance To:
 Author ID: waltman.paul Published as: Waltman, Paul; Waltman, P.; Waltman, P. E.; Waltman, Paul Elvis more...less External Links: MGP
 Documents Indexed: 116 Publications since 1963, including 7 Books Biographic References: 2 Publications Co-Authors: 38 Co-Authors with 93 Joint Publications 744 Co-Co-Authors
all top 5

### Co-Authors

 23 single-authored 15 Freedman, Herbert Irving 11 Hsu, Sze-Bin 11 Smith, Hal Leslie 10 Butler, Geoffrey J. 10 Gatica, Juan A. 7 Bailey, Paul B. 5 Hsu, Szebi 5 Macki, Jack W. 5 Shampine, Lawrence Fred 4 Hoppensteadt, Frank C. 4 Pilyugin, Sergei S. 4 So, Joseph Wai-Hung 3 Hubbell, Stephen P. 3 Oliker, Vladimir I. 2 Fennell, Robert E. 2 Hernandez, Gaston E. 2 Tang, Betty K. P. 2 Utz, Winfried Roy jun. 1 Braselton, James P. 1 Bridgland, T. F. jun. 1 Ellermeyer, Sean F. 1 Fink, Arlington Michael 1 Grimmer, Ronald 1 Hale, Jack Kenneth 1 Hanson, David L. 1 Hethcote, Herbert W. 1 Jäger, Willi 1 Le, Dung 1 Li, Yen-Sheng 1 Luo, Ting-Kung 1 Patula, William T. 1 Rai, Bindhyachal 1 Robertson, Tim 1 Schmid, Rudolf 1 Schrader, Keith W. 1 Suyemoto, Lee 1 Wolkowicz, Gail S. K. 1 Wong, James S. W.
all top 5

### Serials

 15 SIAM Journal on Applied Mathematics 11 Mathematical Biosciences 9 Journal of Mathematical Analysis and Applications 7 Journal of Mathematical Biology 7 Proceedings of the American Mathematical Society 5 Journal of Differential Equations 3 Monatshefte für Mathematik 3 Transactions of the American Mathematical Society 3 SIAM Journal on Mathematical Analysis 2 Rocky Mountain Journal of Mathematics 2 Bulletin of the American Mathematical Society 2 The Bulletin of Mathematical Biophysics 2 Cambridge Studies in Mathematical Biology 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Computation 1 Canadian Mathematical Bulletin 1 Hiroshima Mathematical Journal 1 Indiana University Mathematics Journal 1 Journal of the London Mathematical Society. Second Series 1 Pacific Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Mathematical and Computer Modelling 1 Japan Journal of Industrial and Applied Mathematics 1 SIAM Review 1 The Canadian Applied Mathematics Quarterly 1 Taiwanese Journal of Mathematics 1 Nonlinear Analysis. Real World Applications 1 Journal of Mathematics and Mechanics 1 Journal of Mathematics and Physics 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Lecture Notes in Biomathematics 1 Annals of Mathematical Statistics 1 Nonlinear Analysis. Theory, Methods & Applications
all top 5

### Fields

 68 Biology and other natural sciences (92-XX) 52 Ordinary differential equations (34-XX) 21 Dynamical systems and ergodic theory (37-XX) 10 Partial differential equations (35-XX) 5 Systems theory; control (93-XX) 2 Functional analysis (46-XX) 2 Operator theory (47-XX) 1 Difference and functional equations (39-XX) 1 Numerical analysis (65-XX) 1 Optics, electromagnetic theory (78-XX)

### Citations contained in zbMATH Open

107 Publications have been cited 4,047 times in 2,616 Documents Cited by Year
The theory of the chemostat. Dynamics of microbial competition. Zbl 0860.92031
Smith, Hal L.; Waltman, Paul
1995
Persistence in infinite-dimensional systems. Zbl 0692.34053
Hale, Jack K.; Waltman, Paul
1989
Uniformly persistent systems. Zbl 0603.34043
Butler, Geoffrey; Freedman, H. I.; Waltman, Paul
1986
Persistence in models of three interacting predator-prey populations. Zbl 0534.92026
Freedman, H. I.; Waltman, Paul
1984
A mathematical theory for single-nutrient competition in continuous cultures of micro-organisms. Zbl 0354.92033
Hsu, S. B.; Hubbell, S.; Waltman, P.
1977
Persistence in dynamical systems. Zbl 0603.58033
Butler, Geoffrey; Waltman, Paul
1986
Singular nonlinear boundary value problems for second-order ordinary differential equations. Zbl 0685.34017
Gatica, J. A.; Oliker, Vladimir; Waltman, Paul
1989
Mathematical analysis of some three-species food-chain models. Zbl 0363.92022
Freedman, H. I.; Waltman, Paul
1977
Nonlinear two point boundary value problems. Zbl 0169.10502
Bailey, P. B.; Shampine, L. F.; Waltman, P. E.
1968
Competitive exclusion and coexistence for competitive systems on ordered Banach spaces. Zbl 0860.47033
Hsu, S. B.; Smith, H. L.; Waltman, Paul
1996
A mathematical model of the chemostat with periodic washout rate. Zbl 0584.92027
Butler, G. J.; Hsu, S. B.; Waltman, Paul
1985
Competing predators. Zbl 0394.92025
Hsu, S. B.; Hubbell, S. P.; Waltman, Paul
1978
Persistence in a model of three competitive populations. Zbl 0584.92018
Freedman, H. I.; Waltman, Paul
1985
The theory of the chemostat. Dynamics of microbial competition. Reprint of the 1995 hardback ed. Zbl 1139.92029
Smith, Hal L.; Waltman, Paul
2008
On a system of reaction-diffusion equations arising from competition in an unstirred chemostat. Zbl 0784.92024
Hsu, Sze-Bi; Waltman, P.
1993
Coexistence in a model of competition in the chemostat incorporating discrete delays. Zbl 0676.92013
Freedman, H. I.; So, Joseph W.-H.; Waltman, Paul
1989
Mathematical models of population interactions with dispersal. I: Stability of two habitats with and without a predator. Zbl 0362.92006
Freedman, H. I.; Waltman, Paul
1977
Competition models in population biology. Zbl 0572.92019
Waltman, Paul
1983
Deterministic threshold models in the theory of epidemics. Zbl 0293.92015
Waltman, Paul
1974
Competition in the chemostat when one competitor produces a toxin. Zbl 0982.92035
Hsu, S. B.; Waltman, Paul
1998
Perturbation of a globally stable steady state. Zbl 0924.58087
Smith, H. L.; Waltman, P.
1999
A survey of mathematical models of competition with an inhibitor. Zbl 1034.92034
Hsu, S.-B.; Waltman, Paul
2004
A brief survey of persistence in dynamical systems. Zbl 0756.34054
Waltman, Paul
1991
Analysis of a model of two competitors in a chemostat with an external inhibitor. Zbl 0788.34040
Hsu, S. B.; Waltman, P.
1992
A note on an oscillation criterion for an equation with a functional argument. Zbl 0186.42205
Waltman, P.
1968
Mathematical models of population interactions with dispersal. II: Differential survival in a change of habitat. Zbl 0588.92020
Freedman, H. I.; Rai, Bindhyachal; Waltman, Paul
1986
Coexistence of competing predators in a chemostat. Zbl 0508.92019
Butler, G. J.; Hsu, S. B.; Waltman, P.
1983
Bifurcation from a limit cycle in a two predator-one prey ecosystem modeled on a chemostat. Zbl 0475.92017
Butler, G. J.; Waltman, Paul
1981
Dynamics of competition in the unstirred chemostat. Zbl 0831.92028
Hsu, S. B.; Smith, H. L.; Waltman, Paul
1994
An oscillation criterion for a nonlinear second order equation. Zbl 0131.08902
Waltman, P.
1965
Multiple limit cycles in the chemostat with variable yield. Zbl 1012.92044
Pilyugin, Sergei S.; Waltman, Paul
2003
Competition for a single limiting resource in continuous culture: The variable-yield model. Zbl 0829.92020
Smith, Hal L.; Waltman, Paul
1994
Theoretical and experimental investigations of microbial competition in continuous culture. Zbl 0442.92015
Waltman, Paul; Hubbell, Stephen P.; Hsu, Sze-Bi
1980
On the asymptotic behavior of solutions of a nonlinear equation. Zbl 0131.08901
Waltman, P.
1964
Competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor. Zbl 0835.92028
Hsu, S. B.; Luo, Ting-Kung; Waltman, Paul
1995
On estimating monotone parameters. Zbl 0162.49801
Robertson, T.; Waltman, P.
1968
The simple chemostat with wall growth. Zbl 0934.34042
Pilyugin, Sergei S.; Waltman, Paul
1999
A nonlinear boundary value problem arising from competition in the chemostat. Zbl 0691.92018
So, Joseph W.-H.; Waltman, Paul
1989
Global analysis of a model of plasmid-bearing, plasmid-free competition in a chemostat. Zbl 0802.92027
Hsu, Sze-Bi; Waltman, Paul; Wolkowicz, Gail S. K.
1994
A problem in the theory of epidemics. Zbl 0212.52105
1970
Optimal vaccination schedules in a deterministic model. Zbl 0266.92011
Hethcote, Herbert W.; Waltman, Paul
1973
A competition model with dynamically allocated inhibitor production. Zbl 0984.92033
Braselton, James P.; Waltman, Paul
2001
Competition in the gradostat. Zbl 0643.92021
Jäger, W.; So, Joseph W.-H.; Tang, Betty; Waltman, Paul
1987
Competition in the presence of a lethal external inhibitor. Zbl 1009.92034
Hsu, S. B.; Li, Yen-Sheng; Waltman, Paul
2000
Competition in an $$n$$-vessel gradostat. Zbl 0749.92024
Smith, H. L.; Tang, Betty; Waltman, Paul
1991
A problem in the theory of epidemics. II. Zbl 0226.92011
1971
Competition in the unstirred chemostat with periodic input and washout. Zbl 0991.92035
Pilyugin, Sergei S.; Waltman, Paul
1999
Coexistence in chemostat-like models. Zbl 0721.92026
Waltman, Paul
1990
Approximation of solutions of singular second-order boundary value problems. Zbl 0722.34015
Fink, A. M.; Gatica, Juan A.; Hernandez, Gaston E.; Waltman, Paul
1991
Oscillation criteria for third order nonlinear differential equations. Zbl 0144.11403
Waltman, P.
1966
Some properties of solutions of $$u''+a(t)f(u) = 0$$. Zbl 0116.29401
Waltman, Paul Elvis
1963
The first and second boundary value problems for nonlinear second order differential equations. Zbl 0145.11104
Bailey, P. B.; Shampine, L. F.; Waltman, P.
1966
Radially symmetric solutions of a class of singular elliptic equations. Zbl 0689.35029
Gatica, Juan A.; Hernandez, Gaston E.; Waltman, P.
1990
A remark on the global asymptotic stability of a dynamical system modeling two species competition. Zbl 0806.92016
Hsu, Sze-Bi; Waltman, Paul; Ellermeyer, Sean F.
1994
Predator influence on the growth of a population with three genotypes. Zbl 0393.92012
Freedman, H. I.; Waltman, Paul
1978
On the asymptotic behavior of solutions of an $$n$$-th order equation. Zbl 0138.32302
Waltman, P.
1965
On the distance between consecutive zeros for second order differential equations. Zbl 0142.34703
Bailey, P. B.; Waltman, P.
1966
Existence and uniqueness of solutions of the first boundary value problem for non-linear second order differential equations. Zbl 0152.08602
Bailey, Paul; Waltman, Paul
1966
Asymptotic almost periodicity of solutions of a system of differential equations. Zbl 0166.08701
Utz, W. R.; Waltman, P.
1967
Perturbation of two-dimensional predator-prey equations. Zbl 0313.92001
Freedman, H. I.; Waltman, P.
1975
Oscillation of solutions of a nonlinear equation. Zbl 0137.28402
Waltman, P.
1963
An existence theorem for nonlinear boundary value problems. Zbl 0179.12901
1969
Perturbation of two-dimensional predator-prey equations with an unperturbed critical point. Zbl 0326.92002
Freedman, H. I.; Waltman, P.
1975
The equations of growth. Zbl 0119.35802
Waltman, P. E.
1964
Global dynamics of a selection model for the growth of a population with genotypic fertility differences. Zbl 0499.92017
Butler, G. J.; Freedman, H. I.; Waltman, Paul
1982
A model of the effect of anti-competitor toxins on plasmid-bearing, plasmid-free competition. Zbl 1029.34038
Hsu, Sze-Bi; Waltman, Paul
2002
Existence and uniqueness of solutions of boundary value problems for two dimensional systems of nonlinear differential equations. Zbl 0228.34016
Waltman, Paul
1971
Existence and uniqueness of solutions of a functional differential equation modeling thresholds. Zbl 0586.34055
Gatica, J. A.; Waltman, Paul
1984
Limit point classification of second order linear differential equations. Zbl 0309.34016
Patula, William T.; Waltman, Paul
1974
Periodicity and boundedness of solutions of generalized differential equations of growth. Zbl 0115.37403
Utz, W. R.; Waltman, P. E.
1963
Growth in the unstirred chemostat with different diffusion rates. Zbl 0920.35076
Le Dung; Smith, Hal L.; Waltman, P.
1999
A threshold model of antigen antibody dynamics with fading memory. Zbl 0529.92005
Gatica, J. A.; Waltman, Paul
1982
Extension of a theorem of A. Wintner. Zbl 0127.31102
Suyemoto, L.; Waltman, P.
1963
Existence and uniqueness of solutions of the second order boundary value problem. Zbl 0133.34404
Bailey, P. B.; Shampine, L. F.; Waltman, P.
1966
A boundary value problem for a system of nonlinear functional differential equations. Zbl 0172.12103
Fennell, Robert; Waltman, Paul
1969
Radially symmetric solutions of a Monge-Ampère equation arising in a reflector mapping problem. Zbl 0645.35033
Oliker, V.; Waltman, P.
1987
Two point boundary valu e problems for nonlinear functional differential equations. Zbl 0263.34072
Waltman, Paul; Wong, James S. W.
1972
On convergence of solutions of the forced Lienard equation. Zbl 0137.28301
Waltman, P.; Bridgland, T. F. jun.
1965
A note on a functional equation. Zbl 0138.40004
Hanson, D. L.; Waltman, P.
1965
A comparison theorem for a class of nonlinear differential inequalities. Zbl 0185.17603
Grimmer, R. C.; Waltman, P.
1968
A classification theorem for three dimensional competitive systems. Zbl 0638.34022
Smith, Hal L.; Waltman, Paul
1987
A second course in elementary differential equations. Zbl 0689.34001
Waltman, Paul
1986
Limiting the complexity of limit sets in self-regulating systems. Zbl 0707.92001
Butler, Geoffrey; Schmid, Rudolf; Waltman, Paul
1990
Iterative procedures for nonlinear second order boundary value problems. Zbl 0729.34013
Gatica, J. A.; Oliker, Vladimir; Waltman, Paul
1990
A flow mediated control model of respiration. Zbl 0415.92006
1979
A nonlinear Sturm-Liouville problem. Zbl 0246.34034
Macki, J. W.; Waltman, P.
1972
A nonlinear boundary value problem of Sturm-Liouville type for a two- dimensional system of ordinary differential equations. Zbl 0248.34031
Macki, Jack W.; Waltman, Paul
1971
A second course in elementary differential equations. Reprint of the 1986 original. Zbl 1048.34003
Waltman, Paul
2004
Existence and uniqueness of solutions to a nonlinear boundary value problem. Zbl 0185.16305
Waltman, P.
1968
A system of functional differential equations modeling threshold phenomena. Zbl 0651.34069
Gatica, J. A.; Waltman, P.
1988
Competition in an unstirred multi-dimensional chemostat. Zbl 0934.35074
Smith, Hal L.; Waltman, Paul
1996
Predator influence on the growth of a population with three genotypes. II. Zbl 0525.92014
Freedman, H. I.; Waltman, Paul
1982
A nonlinear boundary value problem. Zbl 0185.16401
Waltman, P.
1968
Periodic solutions of perturbed Lotka-Volterra systems. Zbl 0337.92015
Freedman, H. I.; Waltman, Paul
1975
Competition in the periodic gradostat. Zbl 1004.92036
Smith, H. L.; Waltman, Paul
2000
A deterministic model of the spread of an infection between two populations. Zbl 0298.92008
Waltman, Paul
1972
A threshold criterion for the spread of an infection in a two population model. Zbl 0315.92011
Waltman, Paul
1974
Nonlinear second order boundary value problems. Existence and regions of uniqueness. Zbl 0142.06302
Bailey, P. B.; Shampine, L. F.; Waltman, P.
1966
Persistence in dynamical systems models of three-population ecological communities. Zbl 0623.92025
Butler, G. J.; Freedman, H. I.; Waltman, P.
1987
Boundary value problems for functional differential equations. Zbl 0211.17901
Fennell, Robert; Waltman, Paul
1969
The theory of the chemostat. Dynamics of microbial competition. Reprint of the 1995 hardback ed. Zbl 1139.92029
Smith, Hal L.; Waltman, Paul
2008
A survey of mathematical models of competition with an inhibitor. Zbl 1034.92034
Hsu, S.-B.; Waltman, Paul
2004
A second course in elementary differential equations. Reprint of the 1986 original. Zbl 1048.34003
Waltman, Paul
2004
Multiple limit cycles in the chemostat with variable yield. Zbl 1012.92044
Pilyugin, Sergei S.; Waltman, Paul
2003
Divergence criterion for generic planar systems. Zbl 1094.34035
Pilyugin, Sergei S.; Waltman, Paul
2003
Did something change? Thresholds in population models. Zbl 1056.92058
2003
A model of the effect of anti-competitor toxins on plasmid-bearing, plasmid-free competition. Zbl 1029.34038
Hsu, Sze-Bi; Waltman, Paul
2002
A competition model with dynamically allocated inhibitor production. Zbl 0984.92033
Braselton, James P.; Waltman, Paul
2001
Competition in the presence of a lethal external inhibitor. Zbl 1009.92034
Hsu, S. B.; Li, Yen-Sheng; Waltman, Paul
2000
Competition in the periodic gradostat. Zbl 1004.92036
Smith, H. L.; Waltman, Paul
2000
Perturbation of a globally stable steady state. Zbl 0924.58087
Smith, H. L.; Waltman, P.
1999
The simple chemostat with wall growth. Zbl 0934.34042
Pilyugin, Sergei S.; Waltman, Paul
1999
Competition in the unstirred chemostat with periodic input and washout. Zbl 0991.92035
Pilyugin, Sergei S.; Waltman, Paul
1999
Growth in the unstirred chemostat with different diffusion rates. Zbl 0920.35076
Le Dung; Smith, Hal L.; Waltman, P.
1999
Competition in the chemostat when one competitor produces a toxin. Zbl 0982.92035
Hsu, S. B.; Waltman, Paul
1998
Competitive exclusion and coexistence for competitive systems on ordered Banach spaces. Zbl 0860.47033
Hsu, S. B.; Smith, H. L.; Waltman, Paul
1996
Competition in an unstirred multi-dimensional chemostat. Zbl 0934.35074
Smith, Hal L.; Waltman, Paul
1996
The theory of the chemostat. Dynamics of microbial competition. Zbl 0860.92031
Smith, Hal L.; Waltman, Paul
1995
Competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor. Zbl 0835.92028
Hsu, S. B.; Luo, Ting-Kung; Waltman, Paul
1995
Dynamics of competition in the unstirred chemostat. Zbl 0831.92028
Hsu, S. B.; Smith, H. L.; Waltman, Paul
1994
Competition for a single limiting resource in continuous culture: The variable-yield model. Zbl 0829.92020
Smith, Hal L.; Waltman, Paul
1994
Global analysis of a model of plasmid-bearing, plasmid-free competition in a chemostat. Zbl 0802.92027
Hsu, Sze-Bi; Waltman, Paul; Wolkowicz, Gail S. K.
1994
A remark on the global asymptotic stability of a dynamical system modeling two species competition. Zbl 0806.92016
Hsu, Sze-Bi; Waltman, Paul; Ellermeyer, Sean F.
1994
On a system of reaction-diffusion equations arising from competition in an unstirred chemostat. Zbl 0784.92024
Hsu, Sze-Bi; Waltman, P.
1993
Analysis of a model of two competitors in a chemostat with an external inhibitor. Zbl 0788.34040
Hsu, S. B.; Waltman, P.
1992
A brief survey of persistence in dynamical systems. Zbl 0756.34054
Waltman, Paul
1991
Competition in an $$n$$-vessel gradostat. Zbl 0749.92024
Smith, H. L.; Tang, Betty; Waltman, Paul
1991
Approximation of solutions of singular second-order boundary value problems. Zbl 0722.34015
Fink, A. M.; Gatica, Juan A.; Hernandez, Gaston E.; Waltman, Paul
1991
Coexistence in chemostat-like models. Zbl 0721.92026
Waltman, Paul
1990
Radially symmetric solutions of a class of singular elliptic equations. Zbl 0689.35029
Gatica, Juan A.; Hernandez, Gaston E.; Waltman, P.
1990
Limiting the complexity of limit sets in self-regulating systems. Zbl 0707.92001
Butler, Geoffrey; Schmid, Rudolf; Waltman, Paul
1990
Iterative procedures for nonlinear second order boundary value problems. Zbl 0729.34013
Gatica, J. A.; Oliker, Vladimir; Waltman, Paul
1990
Persistence in infinite-dimensional systems. Zbl 0692.34053
Hale, Jack K.; Waltman, Paul
1989
Singular nonlinear boundary value problems for second-order ordinary differential equations. Zbl 0685.34017
Gatica, J. A.; Oliker, Vladimir; Waltman, Paul
1989
Coexistence in a model of competition in the chemostat incorporating discrete delays. Zbl 0676.92013
Freedman, H. I.; So, Joseph W.-H.; Waltman, Paul
1989
A nonlinear boundary value problem arising from competition in the chemostat. Zbl 0691.92018
So, Joseph W.-H.; Waltman, Paul
1989
A system of functional differential equations modeling threshold phenomena. Zbl 0651.34069
Gatica, J. A.; Waltman, P.
1988
Persistence in three-dimensional Lotka-Volterra systems. Zbl 0632.92019
Butler, G. J.; Waltman, P.
1988
Competition in the gradostat. Zbl 0643.92021
Jäger, W.; So, Joseph W.-H.; Tang, Betty; Waltman, Paul
1987
Radially symmetric solutions of a Monge-Ampère equation arising in a reflector mapping problem. Zbl 0645.35033
Oliker, V.; Waltman, P.
1987
A classification theorem for three dimensional competitive systems. Zbl 0638.34022
Smith, Hal L.; Waltman, Paul
1987
Persistence in dynamical systems models of three-population ecological communities. Zbl 0623.92025
Butler, G. J.; Freedman, H. I.; Waltman, P.
1987
A system of functional differential equations modeling threshold phenomena. Zbl 0652.34072
Gatica, J. A.; Waltman, P.
1987
Uniformly persistent systems. Zbl 0603.34043
Butler, Geoffrey; Freedman, H. I.; Waltman, Paul
1986
Persistence in dynamical systems. Zbl 0603.58033
Butler, Geoffrey; Waltman, Paul
1986
Mathematical models of population interactions with dispersal. II: Differential survival in a change of habitat. Zbl 0588.92020
Freedman, H. I.; Rai, Bindhyachal; Waltman, Paul
1986
A second course in elementary differential equations. Zbl 0689.34001
Waltman, Paul
1986
A mathematical model of the chemostat with periodic washout rate. Zbl 0584.92027
Butler, G. J.; Hsu, S. B.; Waltman, Paul
1985
Persistence in a model of three competitive populations. Zbl 0584.92018
Freedman, H. I.; Waltman, Paul
1985
Persistence in models of three interacting predator-prey populations. Zbl 0534.92026
Freedman, H. I.; Waltman, Paul
1984
Existence and uniqueness of solutions of a functional differential equation modeling thresholds. Zbl 0586.34055
Gatica, J. A.; Waltman, Paul
1984
Competition models in population biology. Zbl 0572.92019
Waltman, Paul
1983
Coexistence of competing predators in a chemostat. Zbl 0508.92019
Butler, G. J.; Hsu, S. B.; Waltman, P.
1983
Global dynamics of a selection model for the growth of a population with genotypic fertility differences. Zbl 0499.92017
Butler, G. J.; Freedman, H. I.; Waltman, Paul
1982
A threshold model of antigen antibody dynamics with fading memory. Zbl 0529.92005
Gatica, J. A.; Waltman, Paul
1982
Predator influence on the growth of a population with three genotypes. II. Zbl 0525.92014
Freedman, H. I.; Waltman, Paul
1982
Bifurcation from a limit cycle in a two predator-one prey ecosystem modeled on a chemostat. Zbl 0475.92017
Butler, G. J.; Waltman, Paul
1981
Theoretical and experimental investigations of microbial competition in continuous culture. Zbl 0442.92015
Waltman, Paul; Hubbell, Stephen P.; Hsu, Sze-Bi
1980
A flow mediated control model of respiration. Zbl 0415.92006
1979
Competing predators. Zbl 0394.92025
Hsu, S. B.; Hubbell, S. P.; Waltman, Paul
1978
Predator influence on the growth of a population with three genotypes. Zbl 0393.92012
Freedman, H. I.; Waltman, Paul
1978
A mathematical theory for single-nutrient competition in continuous cultures of micro-organisms. Zbl 0354.92033
Hsu, S. B.; Hubbell, S.; Waltman, P.
1977
Mathematical analysis of some three-species food-chain models. Zbl 0363.92022
Freedman, H. I.; Waltman, Paul
1977
Mathematical models of population interactions with dispersal. I: Stability of two habitats with and without a predator. Zbl 0362.92006
Freedman, H. I.; Waltman, Paul
1977
A singular functional differential equation arising in an immunological model. Zbl 0348.34053
Gatica, Juan A.; Waltman, Paul
1976
Perturbation of two-dimensional predator-prey equations. Zbl 0313.92001
Freedman, H. I.; Waltman, P.
1975
Perturbation of two-dimensional predator-prey equations with an unperturbed critical point. Zbl 0326.92002
Freedman, H. I.; Waltman, P.
1975
Periodic solutions of perturbed Lotka-Volterra systems. Zbl 0337.92015
Freedman, H. I.; Waltman, Paul
1975
Deterministic threshold models in the theory of epidemics. Zbl 0293.92015
Waltman, Paul
1974
Limit point classification of second order linear differential equations. Zbl 0309.34016
Patula, William T.; Waltman, Paul
1974
A threshold criterion for the spread of an infection in a two population model. Zbl 0315.92011
Waltman, Paul
1974
Optimal vaccination schedules in a deterministic model. Zbl 0266.92011
Hethcote, Herbert W.; Waltman, Paul
1973
Two point boundary valu e problems for nonlinear functional differential equations. Zbl 0263.34072
Waltman, Paul; Wong, James S. W.
1972
A nonlinear Sturm-Liouville problem. Zbl 0246.34034
Macki, J. W.; Waltman, P.
1972
A deterministic model of the spread of an infection between two populations. Zbl 0298.92008
Waltman, Paul
1972
A problem in the theory of epidemics. II. Zbl 0226.92011
1971
Existence and uniqueness of solutions of boundary value problems for two dimensional systems of nonlinear differential equations. Zbl 0228.34016
Waltman, Paul
1971
A nonlinear boundary value problem of Sturm-Liouville type for a two- dimensional system of ordinary differential equations. Zbl 0248.34031
Macki, Jack W.; Waltman, Paul
1971
A nonlinear Sturm-Liouville problem. Zbl 0243.34024
Macki, J. W.; Waltman, P.
1971
A problem in the theory of epidemics. Zbl 0212.52105
1970
An existence theorem for nonlinear boundary value problems. Zbl 0179.12901
1969
A boundary value problem for a system of nonlinear functional differential equations. Zbl 0172.12103
Fennell, Robert; Waltman, Paul
1969
Boundary value problems for functional differential equations. Zbl 0211.17901
Fennell, Robert; Waltman, Paul
1969
Nonlinear two point boundary value problems. Zbl 0169.10502
Bailey, P. B.; Shampine, L. F.; Waltman, P. E.
1968
A note on an oscillation criterion for an equation with a functional argument. Zbl 0186.42205
Waltman, P.
1968
On estimating monotone parameters. Zbl 0162.49801
Robertson, T.; Waltman, P.
1968
A comparison theorem for a class of nonlinear differential inequalities. Zbl 0185.17603
Grimmer, R. C.; Waltman, P.
1968
Existence and uniqueness of solutions to a nonlinear boundary value problem. Zbl 0185.16305
Waltman, P.
1968
A nonlinear boundary value problem. Zbl 0185.16401
Waltman, P.
1968
Asymptotic almost periodicity of solutions of a system of differential equations. Zbl 0166.08701
Utz, W. R.; Waltman, P.
1967
Oscillation criteria for third order nonlinear differential equations. Zbl 0144.11403
Waltman, P.
1966
The first and second boundary value problems for nonlinear second order differential equations. Zbl 0145.11104
Bailey, P. B.; Shampine, L. F.; Waltman, P.
1966
On the distance between consecutive zeros for second order differential equations. Zbl 0142.34703
Bailey, P. B.; Waltman, P.
1966
Existence and uniqueness of solutions of the first boundary value problem for non-linear second order differential equations. Zbl 0152.08602
Bailey, Paul; Waltman, Paul
1966
Existence and uniqueness of solutions of the second order boundary value problem. Zbl 0133.34404
Bailey, P. B.; Shampine, L. F.; Waltman, P.
1966
Nonlinear second order boundary value problems. Existence and regions of uniqueness. Zbl 0142.06302
Bailey, P. B.; Shampine, L. F.; Waltman, P.
1966
An oscillation criterion for a nonlinear second order equation. Zbl 0131.08902
Waltman, P.
1965
On the asymptotic behavior of solutions of an $$n$$-th order equation. Zbl 0138.32302
Waltman, P.
1965
On convergence of solutions of the forced Lienard equation. Zbl 0137.28301
Waltman, P.; Bridgland, T. F. jun.
1965
A note on a functional equation. Zbl 0138.40004
Hanson, D. L.; Waltman, P.
1965
...and 7 more Documents
all top 5

### Cited by 2,696 Authors

 52 Freedman, Herbert Irving 50 Chen, Lansun 45 Waltman, Paul Elvis 38 Zhao, Xiao-Qiang 35 Smith, Hal Leslie 33 Agarwal, Ravi P. 33 Hsu, Szebi 32 Takeuchi, Yasuhiro 30 Wang, Yuanshi 29 Xu, Rui 28 Jiang, Daqing 26 Lou, Yuan 26 Yuan, Sanling 25 Nie, Hua 24 Teng, Zhi-dong 24 Wu, Jianhua 23 Ma, Wanbiao 23 Wang, Feng-Bin 22 Rapaport, Alain 22 Wolkowicz, Gail S. K. 21 O’Regan, Donal 20 Song, Xinyu 19 Chattopadhyay, Joydev 19 Liu, Shengqiang 18 Jiao, Jianjun 18 Ruan, Shigui 18 Sari, Tewfik 17 Cantrell, Robert Stephen 17 Huang, Xuncheng 17 Wang, Wendi 16 Jang, Sophia R.-J. 16 Lam, King-Yeung 16 Mukherjee, Debasis 16 Zhu, Lemin 15 Cui, Jingan 15 Wang, Lin 15 Wong, Patricia J. Y. 15 Wu, Hong 15 Zhang, Tonghua 14 Cai, Shaohong 14 Jiang, Jifa 14 Kuang, Yang 14 Samanta, Sudip K. 13 Ackleh, Azmy S. 13 Cosner, Chris 13 Erbe, Lynn Harry 13 Hallam, Thomas G. 13 Li, Michael Yi 13 Li, Xuezhi 13 Samanta, Guru Prasad 13 Shampine, Lawrence Fred 13 Thieme, Horst R. 13 Wang, Jinliang 13 Wu, Jianhong 13 Xiao, Yanni 13 Zou, Xingfu 12 De Leenheer, Patrick 12 Henderson, Johnny Lee 12 Meng, Xinzhu 12 Qiu, Zhipeng 12 Shi, Junping 11 Butler, Geoffrey J. 11 Gumel, Abba B. 11 Huo, Hai-Feng 11 Jin, Zhen 11 Pang, Guoping 11 Rao, Vadrevu Sree Hari 11 Sun, Shulin 11 Venturino, Ezio 11 Wong, James S. W. 11 Zhang, Long 10 Graef, John R. 10 Harmand, Jérôme 10 Li, Zuxiong 10 Martcheva, Maia 10 Salceanu, Paul Leonard 10 Schreiber, Sebastian J. 10 Shi, Xiangyun 10 Wang, Fengyan 10 Webb, Glenn Francis 10 Yuan, Rong 9 Baxley, John V. 9 Beretta, Edoardo 9 Biswas, Santanu 9 Braselton, James P. 9 Cai, Liming 9 DeAngelis, Donald L. 9 Gatica, Juan A. 9 Grover, James P. 9 Hsu, Sze-Bin 9 Mazenc, Frédéric 9 Pilyugin, Sergei S. 9 Shuai, Zhisheng 9 So, Joseph Wai-Hung 9 Tian, Xiaohong 9 van den Driessche, Pauline 9 Zanolin, Fabio 9 Zhang, Fengqin 9 Zhou, Xueyong 8 Ahmad, Shair ...and 2,596 more Authors
all top 5

### Cited in 277 Serials

 189 Mathematical Biosciences 181 Journal of Mathematical Analysis and Applications 128 Journal of Mathematical Biology 124 Journal of Differential Equations 121 Applied Mathematics and Computation 103 Nonlinear Analysis. Real World Applications 72 Bulletin of Mathematical Biology 72 Discrete and Continuous Dynamical Systems. Series B 66 Nonlinear Analysis. Theory, Methods & Applications 58 Chaos, Solitons and Fractals 44 Proceedings of the American Mathematical Society 44 Journal of Theoretical Biology 43 Mathematical and Computer Modelling 43 Mathematical Biosciences and Engineering 42 Journal of Biological Dynamics 41 International Journal of Biomathematics 39 Computers & Mathematics with Applications 36 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 35 Theoretical Population Biology 34 Journal of Mathematical Chemistry 32 Applied Mathematics Letters 31 Advances in Difference Equations 29 Journal of Computational and Applied Mathematics 29 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 29 Discrete Dynamics in Nature and Society 29 Journal of Biological Systems 27 Applicable Analysis 27 Mathematical Methods in the Applied Sciences 27 Rocky Mountain Journal of Mathematics 27 Applied Mathematical Modelling 24 Journal of Applied Mathematics and Computing 22 Journal of Dynamics and Differential Equations 22 Abstract and Applied Analysis 21 Journal of Difference Equations and Applications 21 Nonlinear Dynamics 20 Physica A 19 Communications in Nonlinear Science and Numerical Simulation 18 Annali di Matematica Pura ed Applicata. Serie Quarta 18 Differential Equations and Dynamical Systems 15 SIAM Journal on Applied Mathematics 14 Monatshefte für Mathematik 13 Acta Applicandae Mathematicae 12 Complexity 12 Journal of Applied Mathematics 12 Journal of Applied Analysis and Computation 11 Transactions of the American Mathematical Society 11 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 11 Discrete and Continuous Dynamical Systems 10 Journal of the Franklin Institute 10 Automatica 10 Acta Mathematicae Applicatae Sinica. English Series 10 Communications on Pure and Applied Analysis 8 Archive for Rational Mechanics and Analysis 8 Mathematics and Computers in Simulation 8 Computational and Applied Mathematics 7 Mathematica Slovaca 7 Mathematical Problems in Engineering 6 Bulletin of the Australian Mathematical Society 6 International Journal of Systems Science 6 Czechoslovak Mathematical Journal 6 Journal of Optimization Theory and Applications 6 Numerische Mathematik 6 Physica D 6 Japan Journal of Industrial and Applied Mathematics 6 SIAM Journal on Applied Dynamical Systems 6 International Journal of Applied and Computational Mathematics 5 Nonlinearity 5 Proceedings of the Edinburgh Mathematical Society. Series II 5 Applied Mathematics and Mechanics. (English Edition) 5 Computational Statistics and Data Analysis 5 Calculus of Variations and Partial Differential Equations 5 Natural Resource Modeling 5 The ANZIAM Journal 5 Boundary Value Problems 5 Mathematical Modelling of Natural Phenomena 5 Discrete and Continuous Dynamical Systems. Series S 5 International Journal of Differential Equations 4 Ricerche di Matematica 4 Applied Numerical Mathematics 4 International Journal of Computer Mathematics 4 Applied Mathematics. Series B (English Edition) 4 Mathematical Modelling and Analysis 4 Advanced Nonlinear Studies 4 Applications and Applied Mathematics 4 Nonlinear Analysis. Hybrid Systems 4 Journal of Nonlinear Science and Applications 4 AIMS Mathematics 3 Ukrainian Mathematical Journal 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Journal of Economic Theory 3 Quarterly of Applied Mathematics 3 Rendiconti del Circolo Matemàtico di Palermo. Serie II 3 Results in Mathematics 3 Tôhoku Mathematical Journal. Second Series 3 Statistics & Probability Letters 3 European Journal of Applied Mathematics 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Aequationes Mathematicae 3 Communications in Statistics. Theory and Methods 3 SIAM Journal on Mathematical Analysis ...and 177 more Serials
all top 5

### Cited in 42 Fields

 1,874 Biology and other natural sciences (92-XX) 1,494 Ordinary differential equations (34-XX) 442 Dynamical systems and ergodic theory (37-XX) 406 Partial differential equations (35-XX) 123 Numerical analysis (65-XX) 91 Systems theory; control (93-XX) 78 Probability theory and stochastic processes (60-XX) 74 Difference and functional equations (39-XX) 68 Operator theory (47-XX) 62 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 59 Calculus of variations and optimal control; optimization (49-XX) 44 Integral equations (45-XX) 27 Statistics (62-XX) 18 Statistical mechanics, structure of matter (82-XX) 13 Computer science (68-XX) 12 Fluid mechanics (76-XX) 11 Real functions (26-XX) 10 Operations research, mathematical programming (90-XX) 9 Combinatorics (05-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Mechanics of particles and systems (70-XX) 5 Approximations and expansions (41-XX) 5 Mechanics of deformable solids (74-XX) 4 History and biography (01-XX) 4 General topology (54-XX) 4 Optics, electromagnetic theory (78-XX) 3 Functional analysis (46-XX) 3 Differential geometry (53-XX) 3 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Abstract harmonic analysis (43-XX) 2 Convex and discrete geometry (52-XX) 2 Mathematics education (97-XX) 1 Mathematical logic and foundations (03-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX)