## Peterson, Allan C.

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 Author ID: peterson.allan-c Published as: Peterson, Allan; Peterson, Allan C.; Peterson, A.; Peterson, A. C.; Peterson, Alan more...less Homepage: https://www.math.unl.edu/~apeterson1/ External Links: MGP
 Documents Indexed: 174 Publications since 1969, including 6 Books 4 Contributions as Editor · 1 Further Contribution Co-Authors: 53 Co-Authors with 149 Joint Publications 2,446 Co-Co-Authors
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### Co-Authors

 26 single-authored 85 Erbe, Lynn Harry 21 Jia, Baoguo 14 Baoguo, Jia 14 Saker, Samir H. 11 Bohner, Martin J. 9 Hassan, Taher S. 7 Hankerson, Darrel R. 7 Ridenhour, Jerry R. 6 Tisdell, Christopher C. 5 Anderson, Douglas Robert 5 Goodrich, Christopher S. 5 Mert, Raziye 4 Ahlbrandt, Calvin D. 4 Du, Feifei 4 Liu, Xiang 4 Mahmoud, Ramy Ramadan 3 Agarwal, Ravi P. 3 Avery, Richard I. 3 Henderson, Johnny Lee 3 Kelley, Walter G. 3 Peil, Timothy 3 Wu, Hongwu 2 Abdeljawad, Thabet 2 Akin, Elvan 2 Elaydi, Saber Nasr 2 Hu, Wei 2 Kaymakçalan, Billur 2 Mathsen, Ronald M. 2 Merdivenci Atici, Ferhan 2 Oganesyan, Gro R. 2 Raffoul, Youssef Naim 2 Řehák, Pavel 2 Schneider, John B. 1 Babuška, Ivo 1 Bullock, John D. 1 Burchett, B. 1 Chen, Churong 1 Chen, Siyuan 1 Ciarlet, Philippe Gaston 1 Diaz, Jerry 1 Eloe, Paul W. 1 Gallagher, Richard Hugo 1 Gensler, Scott 1 Graef, John R. 1 Gritsenko, Valeriĭ Alekseevich 1 Güvenilir, Ayşe Feza 1 Higgins, Raegan J. 1 Huff, S. 1 Krueger, Robert J. 1 Ladas, Gerasimos E. 1 Oden, John Tinsley 1 Olumolode, G. 1 O’Regan, Donal 1 Pennington, Nathan 1 Rheinboldt, Werner C. 1 Sankaran, Gregory Kumar 1 Sukup, Dwight V. 1 Taş, Kenan 1 Thompson, Harold Bevan 1 Tran, Hoainam 1 Wellford, Landon Carter jun. 1 Whiteman, John Robert 1 Zafer, Ağacık 1 Ziekiewicz 1 Zlámal, Miloš A.
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### Serials

 21 Journal of Difference Equations and Applications 15 Journal of Mathematical Analysis and Applications 10 Rocky Mountain Journal of Mathematics 7 Computers & Mathematics with Applications 7 Advances in Difference Equations 6 Journal of Computational and Applied Mathematics 6 Proceedings of the American Mathematical Society 5 Mathematical and Computer Modelling 4 Applied Mathematics and Computation 4 Canadian Mathematical Bulletin 4 Journal of Differential Equations 4 Applied Mathematics Letters 4 Dynamic Systems and Applications 3 Panamerican Mathematical Journal 3 SIAM Journal on Mathematical Analysis 3 The Canadian Applied Mathematics Quarterly 3 Electronic Journal of Differential Equations (EJDE) 3 Mathematical Inequalities & Applications 2 Turkish Journal of Mathematics 2 Discrete and Continuous Dynamical Systems 2 Communications in Applied Analysis 2 Journal of Inequalities and Applications 2 Electronic Journal of Qualitative Theory of Differential Equations 2 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 2 Nonlinear Dynamics and Systems Theory 1 Applicable Analysis 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Archiv der Mathematik 1 Czechoslovak Mathematical Journal 1 Journal of Approximation Theory 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Nachrichten 1 Mathematica Slovaca 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Pacific Journal of Mathematics 1 Quaestiones Mathematicae 1 Differential and Integral Equations 1 Georgian Mathematical Journal 1 Filomat 1 ETNA. Electronic Transactions on Numerical Analysis 1 Methods and Applications of Analysis 1 Dynamics of Continuous, Discrete and Impulsive Systems 1 Differential Equations and Dynamical Systems 1 Cubo Matemática Educacional 1 Journal of Applied Mathematics and Computing 1 Mediterranean Journal of Mathematics 1 Rendiconti del Seminario Matematico. Universitá e Politecnico di Torino 1 Kluwer Texts in the Mathematical Sciences 1 International Journal of Difference Equations 1 Journal of Mathematical Inequalities 1 Applicable Analysis and Discrete Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Applied Analysis and Computation 1 Universitext
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### Fields

 117 Difference and functional equations (39-XX) 96 Ordinary differential equations (34-XX) 27 Real functions (26-XX) 5 General and overarching topics; collections (00-XX) 5 Systems theory; control (93-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Numerical analysis (65-XX) 3 Operator theory (47-XX) 2 History and biography (01-XX) 2 Special functions (33-XX) 2 Integral transforms, operational calculus (44-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX)

### Citations contained in zbMATH Open

159 Publications have been cited 5,919 times in 2,979 Documents Cited by Year
Dynamic equations on time scales. An introduction with applications. Zbl 0978.39001
Bohner, Martin; Peterson, Allan
2001
Advances in dynamic equations on time scales. Zbl 1025.34001
2003
Inequalities on time scales: a survey. Zbl 1021.34005
Agarwal, R.; Bohner, M.; Peterson, A.
2001
Dynamic equations on time scales: A survey. Zbl 1020.39008
Agarwal, Ravi; Bohner, Martin; O’Regan, Donal; Peterson, Allan
2002
Discrete fractional calculus. Zbl 1350.39001
Goodrich, Christopher; Peterson, Allan C.
2015
Difference equations: an introduction with applications. Zbl 0733.39001
Kelley, Walter G.; Peterson, Allan C.
1991
Three positive fixed points of nonlinear operators on ordered Banach spaces. Zbl 1005.47051
Avery, R. I.; Peterson, A. C.
2001
Difference equations. An introduction with applications. 2nd ed. Zbl 0970.39001
Kelley, Walter G.; Peterson, Allan C.
2001
Discrete Hamiltonian systems. Difference equations, continued fractions, and Riccati equations. Zbl 0860.39001
Ahlbrandt, Calvin D.; Peterson, Allan C.
1996
Positive solutions for a nonlinear differential equation on a measure chain. Zbl 0963.34020
Erbe, L.; Peterson, A.
2000
First and second order linear dynamic equations on time scales. Zbl 0993.39010
Bohner, Martin; Peterson, Allan
2001
Oscillation criteria for second-order nonlinear delay dynamic equations. Zbl 1125.34046
Erbe, L.; Peterson, A.; Saker, S. H.
2007
Oscillation criteria for second-order nonlinear dynamic equations on time scales. Zbl 1050.34042
Erbe, Lynn; Peterson, Allan; Saker, S. H.
2003
Green’s functions and comparison theorems for differential equations on measure chains. Zbl 0938.34027
Erbe, Lynn; Peterson, Allan
1999
Oscillation for nonlinear second order dynamic equations on a time scale. Zbl 1061.34018
Bohner, Martin; Erbe, Lynn; Peterson, Allan
2005
Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales. Zbl 1075.39010
Erbe, L.; Peterson, A.; Saker, S. H.
2005
Hille and Nehari type criteria for third-order dynamic equations. Zbl 1128.39009
Erbe, L.; Peterson, A.; Saker, S. H.
2007
The theory of differential equations. Classical and qualitative. 2nd ed. Zbl 1201.34001
Kelley, Walter G.; Peterson, Allan C.
2010
Oscillation criteria for nonlinear damped dynamic equations on time scales. Zbl 1162.39005
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2008
Boundedness and oscillation for nonlinear dynamic equations on a time scale. Zbl 1055.39007
Erbe, Lynn; Peterson, Allan
2004
Comparison theorems for linear dynamic equations on time scales. Zbl 1034.34042
Erbe, Lynn; Peterson, Allan; Řehák, Pavel
2002
Two monotonicity results for nabla and delta fractional differences. Zbl 1327.39011
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
Three positive solutions to a discrete focal boundary value problem. Zbl 1001.39021
Anderson, D.; Avery, R.; Peterson, A.
1998
Oscillation criteria for second-order matrix dynamic equations on a time scale. Zbl 1017.34030
Erbe, Lynn; Peterson, Allan
2002
Convexity for nabla and delta fractional differences. Zbl 1320.39003
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2015
Oscillation criteria for nonlinear functional neutral dynamic equations on time scales. Zbl 1193.34135
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2009
Oscillation criteria for half-linear delay dynamic equations on time scales. Zbl 1173.34037
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H.
2009
Eigenvalue conditions and positive solutions. Zbl 0949.34015
Erbe, Lynn; Peterson, Allan
2000
Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation. Zbl 1145.34329
Erbe, L.; Peterson, A.; Saker, S. H.
2006
Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions. Zbl 1422.39027
Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; Peterson, Allan
2016
Existence-uniqueness for focal-point boundary value problems. Zbl 0473.34009
Peterson, Allan C.
1981
Boundary value problems for an $$n$$th order linear difference equation. Zbl 0532.39001
Peterson, Allan C.
1984
Oscillation of third order nonlinear functional dynamic equations on time scales. Zbl 1213.34116
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2010
Nabla dynamic equations on time scales. Zbl 1032.39007
Anderson, Douglas; Bullock, John; Erbe, Lynn; Peterson, Allan; Tran, Hoainam
2003
Multiple positive solutions of a discrete second order conjugate problem. Zbl 0959.39006
Avery, Richard I.; Peterson, Allan C.
1998
Oscillation of second order linear matrix difference equations. Zbl 0762.39005
Peterson, Allan
1991
Three point boundary value problems on time scales. Zbl 1078.39016
Peterson, A. C.; Raffoul, Y. N.; Tisdell, C. C.
2004
Comparison of eigenvalues for focal point problems for $$n$$-th order difference equations. Zbl 0733.39002
Hankerson, Darrel; Peterson, Allan
1990
A survey of exponential function on times scales. Zbl 1074.39018
Bohner, Martin; Peterson, Allan
2001
On the existence and uniqueness of solutions to boundary value problems on time scales. Zbl 1089.39005
Henderson, Johnny; Peterson, Allan; Tisdell, Christopher C.
2004
Weighted Hardy-type inequalities on time scales with applications. Zbl 1342.26064
Saker, S. H.; Mahmoud, R. R.; Peterson, A.
2016
Exponential stability of dynamic equations on time scales. Zbl 1100.39013
Peterson, Allan C.; Raffoul, Youssef N.
2005
Monotonicity results for delta fractional differences revisited. Zbl 06760211
Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; Peterson, Allan
2017
Monotonicity and convexity for nabla fractional $$(q,h)$$-differences. Zbl 1364.39009
Du, Feifei; Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2016
Henstock-Kurzweil delta and nabla integrals. Zbl 1110.26011
Peterson, Allan; Thompson, Bevan
2006
Existence and uniqueness theorems for nonlinear difference equations. Zbl 0625.39002
Peterson, Allan C.
1987
Discrete linear Hamiltonian systems: A survey. Zbl 0942.39009
Agarwal, Ravi; Ahlbrandt, Calvin; Bohner, Martin; Peterson, Allan
1999
The $$(n,n)$$-disconjugacy of a $$2n$$-th order linear difference equation. Zbl 0815.39003
Ahlbrandt, C. D.; Peterson, A.
1994
Boundedness and uniqueness of solutions to dynamic equations on time scales. Zbl 1072.39017
Peterson, Allan C.; Tisdell, Christopher C.
2004
Kamenev-type oscillation criteria for second-order linear delay dynamic equations. Zbl 1104.34026
Erbe, L.; Peterson, A.; Saker, S. H.
2006
Riccati equations on a measure chain. Zbl 1008.34006
Erbe, Lynn; Peterson, Allan
2001
The $$(2,2)$$-disconjugacy of the fourth order difference equation. Zbl 0837.39004
Peterson, Allan; Ridenhour, Jerry
1995
Laplace transform and $$Z$$-transform: Unification and extension. Zbl 1031.44001
Bohner, Martin; Peterson, Allan
2002
Asymptotic behavior of solutions of a two term difference equation. Zbl 0809.39006
Peil, Timothy; Peterson, Allan
1994
Some relations between the Caputo fractional difference operators and integer-order differences. Zbl 1321.39024
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
Existence, multiplicity and nonexistence of positive solutions to a differential equation on a measure chain. Zbl 0937.34025
Erbe, Lynn; Peterson, Allan; Mathsen, Ronald
2000
Comparison theorems and existence theorems for ordinary differential equations. Zbl 0342.34008
Peterson, Allan C.
1976
Existence-uniqueness for ordinary differential equations. Zbl 0386.34022
Peterson, Allan C.
1978
Green’s functions for focal type boundary value problems. Zbl 0387.34014
Peterson, Allan
1979
Comparison theorems for eigenvalue problems for $$n$$-th order differential equations. Zbl 0692.34020
Hankerson, Darrel; Peterson, Allan
1988
Spectral parameter power series for Sturm-Liouville equations on time scales. Zbl 1245.34088
Erbe, Lynn; Mert, Raziye; Peterson, Allan
2012
Bounds for positive solutions for a focal boundary value problem. Zbl 0933.39040
Atici, F.; Peterson, A.
1998
Oscillation of solution to second-order half-linear delay dynamic equations on time scales. Zbl 1345.34150
Wu, Hongwu; Erbe, Lynn; Peterson, Allan
2016
Oscillation of third order functional dynamic equations with mixed arguments on time scales. Zbl 1213.34115
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2010
On the asymptotic behavior of solutions of Emden-Fowler equations on time scales. Zbl 1259.34093
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2012
Oscillation results for a dynamic equation on a time scale. Zbl 1002.39024
Akin, Elvan; Erbe, Lynn; Peterson, Allan; Kaymakçalan, Billur
2001
Monotonicity and convexity for nabla fractional $$q$$-differences. Zbl 1362.39020
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2016
Kiguradze-type oscillation theorems for second order superlinear dynamic equations on time scales. Zbl 1246.34066
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2011
Hille-Kneser-type criteria for second-order dynamic equations on time scales. Zbl 1229.34136
Erbe, Lynn; Peterson, Allan C.; Saker, Samir H.
2006
Criteria for $$C$$-disfocality of a selfadjoint vector difference equation. Zbl 0802.39003
Peil, Timothy; Peterson, Allan
1993
Oscillation of even order nonlinear delay dynamic equations on time scales. Zbl 1274.34262
Erbe, Lynn; Mert, Raziye; Peterson, Allan; Zafer, Ağacık
2013
Oscillation of an Euler-Cauchy dynamic equation. Zbl 1052.39007
Huff, S.; Olumolode, G.; Pennington, N.; Peterson, A.
2003
Comparison theorems and asymptotic behavior of solutions of discrete fractional equations. Zbl 1349.39006
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
A positivity result applied to difference equations. Zbl 0695.39004
Hankerson, Darrel; Peterson, Allan
1989
Belohorec-type oscillation theorem for second order sublinear dynamic equations on time scales. Zbl 1229.34135
Erbe, Lynn; Jia, Baoguo; Peterson, Allan
2011
Oscillation of second order superlinear dynamic equations with damping on time scales. Zbl 1189.34133
Hassan, Taher S.; Erbe, Lynn; Peterson, Allan
2010
Distribution of zeros of solutions of a fourth order differential equation. Zbl 0183.35901
Peterson, A. C.
1969
Oscillation of $$n$$th order superlinear dynamic equations on time scales. Zbl 1216.34100
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2011
Delay dynamic equations with stability. Zbl 1134.39011
Anderson, Douglas R.; Krueger, Robert J.; Peterson, Allan C.
2006
On the sign of Green’s functions. Zbl 0292.34013
Peterson, Allan C.
1976
Existence of solutions to second-order BVPs on time scales. Zbl 1088.39014
Erbe, Lynn; Peterson, Allan; Tisdell, Christopher C.
2005
Green’s functions for (k,n-k)-boundary value problems for linear difference equations. Zbl 0621.39001
Peterson, Allan C.
1987
Oscillation criteria for a forced second-order nonlinear dynamic equation. Zbl 1168.34025
Erbe, L.; Peterson, A.; Saker, S. H.
2008
Two asymptotic results of solutions for nabla fractional $$(q,h)$$-difference equations. Zbl 1424.39047
Du, Feifei; Erbe, Lynn; Jia, Baoguo; Peterson, Allan
2018
A disconjugacy criterion of W. T. Reid for difference equations. Zbl 0744.34037
Peterson, Allan; Ridenhour, Jerry
1992
A general reduction of order theorem for discrete linear symplectic systems. Zbl 1304.39002
Ahlbrandt, C. D.; Peterson, A. C.
1998
An oscillation theorem for second order superlinear dynamic equations on time scales. Zbl 1297.34100
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2013
Upper bounds for the distances between consecutive zeros of solutions of first order delay differential equations. Zbl 1320.34099
Wu, Hongwu; Erbe, Lynn; Peterson, Allan
2015
Some Bennett-Copson type inequalities on time scales. Zbl 1339.26067
Saker, S. H.; Mahmoud, R. R.; Peterson, A.
2016
Nonoscillation for second order sublinear dynamic equations on time scales. Zbl 1187.34128
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2009
Oscillation and nonoscillation of solutions of second order linear dynamic equations with integrable coefficients on time scales. Zbl 1191.34109
Erbe, Lynn; Jia, Baoguo; Peterson, Allan
2009
A Wong-type oscillation theorem for second order linear dynamic equations on time scales. Zbl 1193.34179
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2010
$$C$$-disfocality for linear Hamiltonian difference systems. Zbl 0818.39003
Peterson, Allan
1994
Disconjugacy for a third order linear difference equation. Zbl 0809.39005
Henderson, J.; Peterson, A.
1994
Comparison theorems for a right disfocal eigenvalue problem. Zbl 0882.34079
Diaz, Jerry; Peterson, Allan
1994
Cauchy functions and Taylor’s formula for time scales $$\mathbb T$$. Zbl 1065.39032
Higgins, Raegan J.; Peterson, Allan
2004
Sturm Liouville equations in the frame of fractional operators with exponential kernels and their discrete versions. Zbl 1429.34007
Abdeljawad, Thabet; Mert, Raziye; Peterson, Allan
2019
A classification of the solutions of a difference equation according to their behavior at infinity. Zbl 0664.39001
Hankerson, Darrel; Peterson, Allan
1988
A theorem of Aliev. Zbl 0184.11701
Peterson, A. C.
1969
Asymptotic properties of solutions to a $$2n$$th-order differential equation on a time scale. Zbl 0963.34042
Anderson, D.; Peterson, A.
2000
A Sturm-Liouville approach for continuous and discrete Mittag-Leffler kernel fractional operators. Zbl 1491.34018
Mert, Raziye; Abdeljawad, Thabet; Peterson, Allan
2021
Sturm Liouville equations in the frame of fractional operators with exponential kernels and their discrete versions. Zbl 1429.34007
Abdeljawad, Thabet; Mert, Raziye; Peterson, Allan
2019
Gronwall’s inequality for a nabla fractional difference system with a retarded argument and an application. Zbl 1429.39004
Chen, Churong; Mert, Raziye; Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2019
A generalized $$h$$-fractional Gronwall’s inequality and its applications for nonlinear $$h$$-fractional difference systems with ‘maxima’. Zbl 1421.39002
Liu, Xiang; Peterson, Allan; Jia, Baoguo; Erbe, Lynn
2019
Asymptotic behavior of solutions of fractional nabla $$q$$-difference equations. Zbl 1414.39003
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2019
Stability analysis for a class of nabla $$(q,h)$$-fractional difference equations. Zbl 1410.39030
Liu, Xiang; Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2019
Two asymptotic results of solutions for nabla fractional $$(q,h)$$-difference equations. Zbl 1424.39047
Du, Feifei; Erbe, Lynn; Jia, Baoguo; Peterson, Allan
2018
A unified approach to Copson and Beesack type inequalities on time scales. Zbl 1403.26023
Saker, S. H.; Mahmoud, R. R.; Peterson, A.
2018
Asymptotic behavior of nabla half order $$h$$-difference equations. Zbl 1457.39005
Jia, Baoguo; Du, Feifei; Erbe, Lynn; Peterson, Allan
2018
Monotonicity results for delta fractional differences revisited. Zbl 06760211
Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; Peterson, Allan
2017
The relation between nabla fractional differences and nabla integer differences. Zbl 1488.26011
Baoguo, Jia; Erbe, Lynn; Goodrich, Christopher; Peterson, Allan
2017
Liapunov functional and stability of linear nabla $$(q,h)$$-fractional difference equations. Zbl 1406.39021
Jia, Baoguo; Chen, Siyuan; Erbe, Lynn; Peterson, Allan
2017
Existence and rapid convergence results for nonlinear Caputo nabla fractional difference equations. Zbl 1413.39009
Liu, Xiang; Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2017
Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions. Zbl 1422.39027
Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; Peterson, Allan
2016
Weighted Hardy-type inequalities on time scales with applications. Zbl 1342.26064
Saker, S. H.; Mahmoud, R. R.; Peterson, A.
2016
Monotonicity and convexity for nabla fractional $$(q,h)$$-differences. Zbl 1364.39009
Du, Feifei; Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2016
Oscillation of solution to second-order half-linear delay dynamic equations on time scales. Zbl 1345.34150
Wu, Hongwu; Erbe, Lynn; Peterson, Allan
2016
Monotonicity and convexity for nabla fractional $$q$$-differences. Zbl 1362.39020
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2016
Some Bennett-Copson type inequalities on time scales. Zbl 1339.26067
Saker, S. H.; Mahmoud, R. R.; Peterson, A.
2016
Oscillation criteria for second order sublinear dynamic equations with oscillating coefficients. Zbl 1347.34140
Wu, Hongwu; Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2016
Discrete fractional calculus. Zbl 1350.39001
Goodrich, Christopher; Peterson, Allan C.
2015
Two monotonicity results for nabla and delta fractional differences. Zbl 1327.39011
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
Convexity for nabla and delta fractional differences. Zbl 1320.39003
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2015
Some relations between the Caputo fractional difference operators and integer-order differences. Zbl 1321.39024
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
Comparison theorems and asymptotic behavior of solutions of discrete fractional equations. Zbl 1349.39006
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
Upper bounds for the distances between consecutive zeros of solutions of first order delay differential equations. Zbl 1320.34099
Wu, Hongwu; Erbe, Lynn; Peterson, Allan
2015
A new Picone’s dynamic inequality on time scales with applications. Zbl 1323.26029
Saker, S. H.; Mahmoud, R. R.; Peterson, A.
2015
Nabla discrete fractional Grüss type inequality. Zbl 1372.39010
Güvenilir, A. Feza; Kaymakçalan, Billur; Peterson, Allan C.; Taş, Kenan
2014
A Butler-type oscillation theorem for second-order dynamic equations on discrete timescales. Zbl 1304.34160
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2014
Oscillation of even order nonlinear delay dynamic equations on time scales. Zbl 1274.34262
Erbe, Lynn; Mert, Raziye; Peterson, Allan; Zafer, Ağacık
2013
An oscillation theorem for second order superlinear dynamic equations on time scales. Zbl 1297.34100
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2013
Spectral parameter power series for Sturm-Liouville equations on time scales. Zbl 1245.34088
Erbe, Lynn; Mert, Raziye; Peterson, Allan
2012
On the asymptotic behavior of solutions of Emden-Fowler equations on time scales. Zbl 1259.34093
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2012
Oscillation theorems for second order sublinear dynamic equations on time scales. Zbl 1269.34073
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2012
Asymptotic behavior of $$n$$-th order dynamic equations. Zbl 1279.34106
Erbe, L.; Hovhannisyan, G.; Peterson, A.
2012
Kiguradze-type oscillation theorems for second order superlinear dynamic equations on time scales. Zbl 1246.34066
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2011
Belohorec-type oscillation theorem for second order sublinear dynamic equations on time scales. Zbl 1229.34135
Erbe, Lynn; Jia, Baoguo; Peterson, Allan
2011
Oscillation of $$n$$th order superlinear dynamic equations on time scales. Zbl 1216.34100
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2011
Oscillation criteria for second order sublinear dynamic equations with damping term. Zbl 1228.34146
Hassan, Taher S.; Erbe, Lynn; Peterson, Allan
2011
Asymptotic behavior of $$n$$-th order sublinear dynamic equations on time scales. Zbl 1235.34239
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2011
The theory of differential equations. Classical and qualitative. 2nd ed. Zbl 1201.34001
Kelley, Walter G.; Peterson, Allan C.
2010
Oscillation of third order nonlinear functional dynamic equations on time scales. Zbl 1213.34116
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2010
Oscillation of third order functional dynamic equations with mixed arguments on time scales. Zbl 1213.34115
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2010
Oscillation of second order superlinear dynamic equations with damping on time scales. Zbl 1189.34133
Hassan, Taher S.; Erbe, Lynn; Peterson, Allan
2010
A Wong-type oscillation theorem for second order linear dynamic equations on time scales. Zbl 1193.34179
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2010
Interval oscillation criteria for forced second-order nonlinear delay dynamic equations with oscillatory potential. Zbl 1202.34162
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H.
2010
Oscillation of sublinear Emden-Fowler dynamic equations on time scales. Zbl 1191.34107
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2010
Oscillation criteria for nonlinear functional neutral dynamic equations on time scales. Zbl 1193.34135
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2009
Oscillation criteria for half-linear delay dynamic equations on time scales. Zbl 1173.34037
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H.
2009
Nonoscillation for second order sublinear dynamic equations on time scales. Zbl 1187.34128
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2009
Oscillation and nonoscillation of solutions of second order linear dynamic equations with integrable coefficients on time scales. Zbl 1191.34109
Erbe, Lynn; Jia, Baoguo; Peterson, Allan
2009
Oscillation of a family of $$q$$-difference equations. Zbl 1170.39002
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2009
Oscillation criteria for first order forced dynamic equations. Zbl 1299.34293
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2009
Oscillation criteria for nonlinear damped dynamic equations on time scales. Zbl 1162.39005
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2008
Oscillation criteria for a forced second-order nonlinear dynamic equation. Zbl 1168.34025
Erbe, L.; Peterson, A.; Saker, S. H.
2008
Basic existence, uniqueness and approximation results for positive solutions to nonlinear dynamic equations on time scales. Zbl 1158.34025
Erbe, L.; Peterson, A.; Tisdell, Christopher C.
2008
New comparison and oscillation theorems for second-order half-linear dynamic equations on time scales. Zbl 1165.34340
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2008
Oscillation criteria for second-order nonlinear delay dynamic equations. Zbl 1125.34046
Erbe, L.; Peterson, A.; Saker, S. H.
2007
Hille and Nehari type criteria for third-order dynamic equations. Zbl 1128.39009
Erbe, L.; Peterson, A.; Saker, S. H.
2007
Recent results concerning dynamic equations on time scales. Zbl 1177.34008
Erbe, Lynn; Peterson, Allan
2007
Some new comparison results for second order linear dynamic equations. Zbl 1201.34142
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2007
Integral comparison theorems for second-order linear dynamic equations. Zbl 1127.39029
Erbe, Lynn; Peterson, Allan; Řehák, Pavel
2007
Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation. Zbl 1145.34329
Erbe, L.; Peterson, A.; Saker, S. H.
2006
Henstock-Kurzweil delta and nabla integrals. Zbl 1110.26011
Peterson, Allan; Thompson, Bevan
2006
Kamenev-type oscillation criteria for second-order linear delay dynamic equations. Zbl 1104.34026
Erbe, L.; Peterson, A.; Saker, S. H.
2006
Hille-Kneser-type criteria for second-order dynamic equations on time scales. Zbl 1229.34136
Erbe, Lynn; Peterson, Allan C.; Saker, Samir H.
2006
Delay dynamic equations with stability. Zbl 1134.39011
Anderson, Douglas R.; Krueger, Robert J.; Peterson, Allan C.
2006
Monotone solutions of dynamic systems on time scales. Zbl 1098.39010
Erbe, L.; Peterson, A.; Tisdell, C. C.
2006
Oscillation for nonlinear second order dynamic equations on a time scale. Zbl 1061.34018
Bohner, Martin; Erbe, Lynn; Peterson, Allan
2005
Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales. Zbl 1075.39010
Erbe, L.; Peterson, A.; Saker, S. H.
2005
Exponential stability of dynamic equations on time scales. Zbl 1100.39013
Peterson, Allan C.; Raffoul, Youssef N.
2005
Existence of solutions to second-order BVPs on time scales. Zbl 1088.39014
Erbe, Lynn; Peterson, Allan; Tisdell, Christopher C.
2005
Square integrability of Gaussian bells on time scales. Zbl 1088.81058
Erbe, L.; Peterson, A.; Simon, M.
2005
Comparison theorems of Hille-Wintner type for dynamic equations on time scales. Zbl 1078.39015
Erbe, Lynn; Peterson, Allan
2005
Boundedness and oscillation for nonlinear dynamic equations on a time scale. Zbl 1055.39007
Erbe, Lynn; Peterson, Allan
2004
Three point boundary value problems on time scales. Zbl 1078.39016
Peterson, A. C.; Raffoul, Y. N.; Tisdell, C. C.
2004
On the existence and uniqueness of solutions to boundary value problems on time scales. Zbl 1089.39005
Henderson, Johnny; Peterson, Allan; Tisdell, Christopher C.
2004
Boundedness and uniqueness of solutions to dynamic equations on time scales. Zbl 1072.39017
Peterson, Allan C.; Tisdell, Christopher C.
2004
Cauchy functions and Taylor’s formula for time scales $$\mathbb T$$. Zbl 1065.39032
Higgins, Raegan J.; Peterson, Allan
2004
Some recent results in linear and nonlinear oscillation. Zbl 1073.34033
Erbe, Lynn; Peterson, Allan
2004
Advances in dynamic equations on time scales. Zbl 1025.34001
2003
Oscillation criteria for second-order nonlinear dynamic equations on time scales. Zbl 1050.34042
Erbe, Lynn; Peterson, Allan; Saker, S. H.
2003
Nabla dynamic equations on time scales. Zbl 1032.39007
Anderson, Douglas; Bullock, John; Erbe, Lynn; Peterson, Allan; Tran, Hoainam
2003
Oscillation of an Euler-Cauchy dynamic equation. Zbl 1052.39007
Huff, S.; Olumolode, G.; Pennington, N.; Peterson, A.
2003
An oscillation result for a nonlinear dynamic equation on a time scale. Zbl 1086.39004
Erbe, Lynn; Peterson, Allan
2003
Dynamic equations on time scales: A survey. Zbl 1020.39008
Agarwal, Ravi; Bohner, Martin; O&rsquo;Regan, Donal; Peterson, Allan
2002
Comparison theorems for linear dynamic equations on time scales. Zbl 1034.34042
Erbe, Lynn; Peterson, Allan; Řehák, Pavel
2002
Oscillation criteria for second-order matrix dynamic equations on a time scale. Zbl 1017.34030
Erbe, Lynn; Peterson, Allan
2002
Laplace transform and $$Z$$-transform: Unification and extension. Zbl 1031.44001
Bohner, Martin; Peterson, Allan
2002
Averaging techniques for self-adjoint matrix equations on a measure chain. Zbl 1014.39005
Erbe, Lynn; Peterson, Allan
2002
Existence of bounded solutions for second order dynamic equations. Zbl 1005.39018
Akin, Elvan; Bohner, Martin; Erbe, Lynn; Peterson, Allan
2002
Prediction of swerving motion of a dual-spin projectile with lateral pulse jets in atmospheric flight. Zbl 1054.70021
Burchett, B.; Peterson, A.; Costello, M.
2002
Dynamic equations on time scales. An introduction with applications. Zbl 0978.39001
Bohner, Martin; Peterson, Allan
2001
Inequalities on time scales: a survey. Zbl 1021.34005
Agarwal, R.; Bohner, M.; Peterson, A.
2001
Three positive fixed points of nonlinear operators on ordered Banach spaces. Zbl 1005.47051
Avery, R. I.; Peterson, A. C.
2001
Difference equations. An introduction with applications. 2nd ed. Zbl 0970.39001
Kelley, Walter G.; Peterson, Allan C.
2001
First and second order linear dynamic equations on time scales. Zbl 0993.39010
Bohner, Martin; Peterson, Allan
2001
A survey of exponential function on times scales. Zbl 1074.39018
Bohner, Martin; Peterson, Allan
2001
Riccati equations on a measure chain. Zbl 1008.34006
Erbe, Lynn; Peterson, Allan
2001
Oscillation results for a dynamic equation on a time scale. Zbl 1002.39024
Akin, Elvan; Erbe, Lynn; Peterson, Allan; Kaymakçalan, Billur
2001
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