# zbMATH — the first resource for mathematics

## Troy, William C.

Compute Distance To:
 Author ID: troy.william-c Published as: Troy, W.; Troy, W. C.; Troy, William; Troy, William C.
 Documents Indexed: 108 Publications since 1976, including 1 Book
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#### Co-Authors

 31 single-authored 21 Peletier, Lambertus Adrianus 14 Hastings, Stuart P. 9 McLeod, John Bryce 6 Ermentrout, George Bard 4 Klaasen, Gene A. 3 Laing, Carlo R. 3 Rajagopal, Kumbakonam Ramamani 2 Aftalion, Amandine 2 Bebernes, Jerrold W. 2 Hale, Jack Kenneth 2 Krisner, Edward P. 2 Kwong, Man Kam 2 Lu, Chunqing 2 Mizel, Victor J. 2 Rinzel, John 2 Rotariu-Bruma, A. I. 2 Stuart, Charles Alexander 1 Anderson, Stewart J. 1 Caginalp, Gunduz 1 Chen, Xinfu 1 Eberly, Dave 1 Ermentrout, Bard G. 1 Field, Richard J. 1 González Llorente, José 1 Gutkin, Boris S. 1 Hassard, Brian D. 1 Jones, James A. 1 Jones, James D. 1 Kazarinoff, Nicholas D. 1 Keener, James P. 1 Kneezel, Timothy 1 MacGillivary, A. D. 1 Manfredi, Juan J. 1 Massoudi, Mehrdad 1 McLeod, Kevin 1 Merdan, Hüseyin 1 Overman, Edward A. II 1 Paullet, Joseph Edward 1 Pinto, David J. 1 Raghavan, Serugudi V. 1 Rubin, Jonathan E. 1 Shusterman, Vladimir 1 Sweers, Guido H. 1 Szeri, Andras Z. 1 van den Berg, Jan Bouwe 1 Vandervorst, Robertus C. A. M. 1 Weissler, Fred B. 1 Wineman, Alan S. 1 Wu, Jang-Mei 1 Zhang, Jianhe
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#### Serials

 15 Journal of Differential Equations 12 SIAM Journal on Applied Mathematics 12 SIAM Journal on Mathematical Analysis 7 Quarterly of Applied Mathematics 7 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 6 Archive for Rational Mechanics and Analysis 4 Journal of Mathematical Analysis and Applications 4 Rocky Mountain Journal of Mathematics 4 SIAM Journal on Applied Dynamical Systems 3 Physica D 3 European Journal of Applied Mathematics 3 Differential and Integral Equations 2 Applied Mathematics Letters 2 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 International Journal of Non-Linear Mechanics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Arabian Journal for Science and Engineering 1 Differential Equations 1 International Journal of Mathematics and Mathematical Sciences 1 CWI Quarterly 1 European Journal of Mechanics. B. Fluids 1 Proceedings of the Royal Irish Academy. Section A, Mathematical and Physical Sciences 1 Bulletin of the American Mathematical Society. New Series 1 Topological Methods in Nonlinear Analysis 1 Electronic Journal of Differential Equations (EJDE) 1 RIMS Kokyuroku 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 International Journal of Pure and Applied Mathematics 1 International Journal of Differential Equations 1 Progress in Nonlinear Differential Equations and Their Applications
all top 5

#### Fields

 60 Ordinary differential equations (34-XX) 49 Partial differential equations (35-XX) 22 Biology and other natural sciences (92-XX) 15 Fluid mechanics (76-XX) 8 Integral equations (45-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Mechanics of deformable solids (74-XX) 5 Numerical analysis (65-XX) 3 Optics, electromagnetic theory (78-XX) 3 Geophysics (86-XX) 2 Probability theory and stochastic processes (60-XX) 2 Quantum theory (81-XX) 1 General and overarching topics; collections (00-XX) 1 Real functions (26-XX) 1 Difference and functional equations (39-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH

85 Publications have been cited 1,270 times in 921 Documents Cited by Year
Symmetry properties in systems of semilinear elliptic equations. Zbl 0486.35032
Troy, William C.
1981
Spatial patterns. Higher order models in physics and mechanics. Zbl 1076.34515
Peletier, L. A.; Troy, W. C.
2001
Multiple bumps in a neuronal model of working memory. Zbl 1017.45006
Laing, Carlo R.; Troy, William C.; Gutkin, Boris; Ermentrout, G. Bard
2002
PDE methods for nonlocal models. Zbl 1088.34011
Laing, Carlo R.; Troy, William C.
2003
An existence theorem for the flow of a non-Newtonian fluid past an infinite porous plate. Zbl 0599.76013
Rajagopal, K. R.; Szeri, A. Z.; Troy, W.
1986
Spatial patterns described by the extended Fisher-Kolmogorov equation: Periodic solutions. Zbl 0891.34048
Peletier, L. A.; Troy, W. C.
1997
Uniqueness of flow of a second-order fluid past a stretching sheet. Zbl 0613.76006
Troy, William C.; Overman, Edward A. II; Ermentrout, G. B.; Keener, James P.
1987
Stationary solutions of a fourth order nonlinear diffusion equation. Zbl 0856.35029
Peletier, L. A.; Troy, W. C.; van der Vorst, R. C. A. M.
1995
A topological shooting method and the existence of kinks of the extended Fisher-Kolmogorov equation. Zbl 0862.34030
Peletier, L. A.; Troy, W. C.
1995
Exact homoclinic and heteroclinic solutions of the Gray-Scott model for autocatalysis. Zbl 0965.34037
Hale, J. K.; Peletier, L. A.; Troy, W. C.
2000
Two-bump solutions of Amari-type models of neuronal pattern formation. Zbl 1011.92007
Laing, Carlo R.; Troy, William C.
2003
Spatial patterns described by the extended Fisher-Kolmogorov (EFK) equation: Kinks. Zbl 0826.34056
Peletier, L. A.; Troy, W. C.
1995
Radial solutions of $$\Delta u+f(u)=0$$ with prescribed numbers of zeros. Zbl 0695.34020
McLeod, Kevin; Troy, W. C.; Weissler, F. B.
1990
Chaotic spatial patterns described by the extended Fisher-Kolmogorov equation. Zbl 0862.34012
Peletier, L. A.; Troy, W. C.
1996
Global branches of multi-bump periodic solutions of the Swift-Hohenberg equation. Zbl 0983.34032
van den Berg, G. J. B.; Peletier, L. A.; Troy, W. C.
2001
Spatial patterns in higher order phase transitions. Zbl 0872.34032
Peletier, L. A.; Troy, W. C.
1996
Solutions of third-order differential equations relevant to draining and coating flows. Zbl 0807.34030
Troy, William C.
1993
The existence of bounded solutions of a semilinear heat equation. Zbl 0655.35039
Troy, William C.
1987
The existence of traveling wave front solutions of a model of the Belousov-Zhabotinskii chemical reaction. Zbl 0429.34025
Troy, William C.
1980
Periodic phases in second-order materials. Zbl 0931.74006
Mizel, V. J.; Peletier, L. A.; Troy, W. C.
1998
Stability and instability in the Gray-Scott model: The case of equal diffusivities. Zbl 0936.92034
Hale, J. K.; Peletier, L. A.; Troy, W. C.
1999
On ground state solutions of $$-\Delta{} u=u^ p-u^ q$$. Zbl 0778.35039
Kwong, M. K.; McLeod, J. B.; Peletier, L. A.; Troy, W. C.
1992
Sustained spatial patterns of activity in neuronal populations without recurrent excitation. Zbl 1075.45011
Rubin, Jonathan E.; Troy, William C.
2004
The existence of spiral waves in an oscillatory reaction-diffusion system. Zbl 0823.92003
Paullet, Joseph; Ermentrout, Bard; Troy, William
1994
Stationary wave solutions of a system of reaction-diffusion equations derived from the FitzHugh-Nagumo equations. Zbl 0543.35051
Klaasen, Gene A.; Troy, William C.
1984
A computer proof that the Lorenz equations have “chaotic” solutions. Zbl 0792.65050
Hassard, B.; Zhang, J.; Hastings, S. P.; Troy, W. C.
1994
A shooting approach to the Lorenz equations. Zbl 0764.58023
Hastings, S. P.; Troy, W. C.
1992
Bifurcation phenomena in FitzHugh’s nerve conduction equations. Zbl 0329.92001
Troy, William C.
1976
On the bifurcation curve for an elliptic system of FitzHugh-Nagumo type. Zbl 1082.35068
Sweers, Guido; Troy, William C.
2003
A proof that the Lorenz equations have a homoclinic orbit. Zbl 0807.34059
Hastings, S. P.; Troy, W. C.
1994
Nonexistence for the Kassoy problem. Zbl 0645.34008
Bebernes, J.; Troy, W.
1987
A shooting approach to chaos in the Lorenz equations. Zbl 0849.34031
Hastings, S. P.; Troy, W. C.
1996
Existence of logarithmic-type solutions to the Kapila-Kassoy problem in dimensions 3 through 9. Zbl 0648.34018
Eberly, D.; Troy, W. C.
1987
Multibump periodic travelling waves in suspension bridges. Zbl 0909.35143
Peletier, L. A.; Troy, W. C.
1998
Existence of solutions to the equations governing the flow of granular materials. Zbl 0755.76012
Rajagopal, K. R.; Troy, W.; Massoudi, M.
1992
The existence of steady solutions of the Kuramoto-Sivashinsky equation. Zbl 0693.34053
Troy, William C.
1989
Oscillating solutions of the Falkner-Skan for positive $$\beta$$. Zbl 0703.34044
Hastings, S. P.; Troy, W. C.
1988
The bifurcation of periodic solutions in the Hodgkin-Huxley equations. Zbl 0403.35090
Troy, William C.
1978
On the solutions of the one-dimensional Ginzburg-Landau equations for superconductivity. Zbl 0946.34023
Aftalion, Amandine; Troy, William C.
1999
Large amplitude stationary waves in an excitable lateral-inhibitory medium. Zbl 0561.92001
Ermentrout, G. B.; Hastings, S. P.; Troy, W. C.
1984
The stability of traveling wave front solutions of a reaction-diffusion system. Zbl 0467.35011
Klaasen, Gene A.; Troy, William C.
1981
Oscillation phenomena in the Hodgkin-Huxley equations. Zbl 0373.34019
Troy, William C.
1976
The asymptotic behavior of solutions of a system of reaction-diffusion equations which models the Belousov-Zhabotinskii chemical reaction. Zbl 0467.35015
Klaasen, Gene A.; Troy, William C.
1981
Pulse-like spatial patterns described by higher-order model equations. Zbl 0920.34048
Peletier, L. A.; Rotariu-Bruma, A. I.; Troy, W. C.
1998
The existence of multiple solutions for a Ginzburg-Landau type model of superconductivity. Zbl 0880.34023
Hastings, S. P.; Kwong, M. K.; Troy, W. C.
1996
A one-variable map analysis of bursting in the Belousov-Zhabotinskii reaction. Zbl 0514.34033
Rinzel, John; Troy, William C.
1983
Uniqueness of positive ground state solutions of the logarithmic Schrödinger equation. Zbl 1348.35247
Troy, William C.
2016
Patterns and features of families of traveling waves in large-scale neuronal networks. Zbl 1210.34030
2007
There are asymmetric minimizers for the one-dimensional Ginzburg–Landau model of superconductivity. Zbl 0923.34019
Hastings, Stuart P.; Troy, William C.
1999
The Skyrme model for nucleons under spherical symmetry. Zbl 0734.34023
McLeod, J. B.; Troy, W. C.
1991
On some conjectures of Turcotte, Spence, Bau, and Holmes. Zbl 0704.34027
Hastings, S. P.; Troy, W. C.
1989
Oscillating solutions of the Falkner-Skan equation for negative $$\beta$$. Zbl 0621.76033
Hastings, S. P.; Troy, W. C.
1987
The role of Painleve II in predicting new liquid crystal self-assembly mechanisms. Zbl 1393.35210
Troy, William C.
2018
Traveling waves and synchrony in an excitable large-scale neuronal network with asymmetric connections. Zbl 1166.45006
Troy, William C.
2008
The existence and uniqueness of bound-state solutions of a semi-linear equation. Zbl 1186.34038
Troy, W. C.
2005
Stability of standing waves for some nonlinear Schrödinger equations. Zbl 1037.34022
McLeod, J. B.; Stuart, C. A.; Troy, W. C.
2003
Pattern formation described by the Swift-Hohenberg equation. Zbl 1058.35528
Peletier, L. A.; Troy, W. C.
2000
An exact reduction of Maxwell’s equations. Zbl 0797.34035
McLeod, J. B.; Stuart, C. A.; Troy, W. C.
1992
Steady solutions of the Kuramoto-Sivashinsky equation for small wave speed. Zbl 0745.34037
Jones, J.; Troy, W. C.; MacGillivary, A. D.
1992
Nonexistence of monotone solutions in a model of dendritic growth. Zbl 0701.34046
Troy, William C.
1990
Existence of solutions of the similarity equations for floating rectangular cavities and disks. Zbl 0657.76032
Lu, Chunqing; Kazarinoff, Nicholas D.; McLeod, J. Bryce; Troy, William C.
1988
A note on non-universal deformations of nonlinear elastic layers. Zbl 0613.73036
Rajagopal, K. R.; Troy, W. C.; Wineman, A. S.
1986
Phaselocking in a reaction-diffusion system with a linear frequency gradient. Zbl 0606.92012
Ermentrout, G. B.; Troy, W. C.
1986
Oscillatory solutions of the Falkner-Skan equation. Zbl 0586.76049
Hastings, S. P.; Troy, W.
1985
The existence of solitary traveling wave solutions of a model of the Belousov-Zhabotinskii reaction. Zbl 0449.35091
Field, Richard J.; Troy, William C.
1979
Non-monotonic solutions of the Falkner-Skan boundary layer equation. Zbl 0423.76028
Troy, William C.
1979
Asymmetric activity waves in synaptic cortical systems. Zbl 1171.92012
Pinto, David J.; Troy, William; Kneezel, Timothy
2009
Self-similar solutions for infiltration of dopant into semiconductors. Zbl 0752.35029
Peletier, L. A.; Troy, W. C.
1991
On nonexistence of similarity solutions. Zbl 0673.35045
Peletier, L. A.; Troy, W. C.
1988
Oscillations in a third order differential equation modeling a nuclear reactor. Zbl 0349.34030
Troy, William C.
1977
Existence and exact multiplicity of phaselocked solutions of a Kuramoto model of mutually coupled oscillators. Zbl 1322.45005
Troy, William C.
2015
Self-similar solutions for diffusion in semiconductors. Zbl 0811.35146
Peletier, L. A.; Troy, W. C.
1994
Bounded solutions of $$\Delta u+|u|^{p-1}u-|u|^{q-1}u=0$$ in the supercritical case. Zbl 0736.34026
Troy, William C.
1990
The uniqueness and stability of the rest state for strongly coupled oscillators. Zbl 0701.35019
Ermentrout, G. Bard; Troy, William C.
1989
The behavior of solutions of a nonlinear boundary layer equation. Zbl 0652.76015
Lu, Chunqing; Troy, William C.
1988
On $$p$$-harmonic measures in half-spaces. Zbl 1432.35100
Llorente, José G.; Manfredi, Juan J.; Troy, William C.; Wu, Jang-Mei
2019
Bifurcation analysis of a single-group asset flow model. Zbl 1403.91390
Merdan, H.; Caginalp, G.; Troy, W. C.
2016
Wave phenomena in neuronal networks. Zbl 1218.92025
Troy, W. C.
2008
Boundary value problems in the Fanno model for turbulent compressible flow. Zbl 1007.76029
Hastings, S. P.; McLeod, J. B.; Troy, W. C.
2002
On the Opial-Olech-Beesack inequalities. Zbl 0979.26011
Troy, William C.
2001
On the uniqueness of solutions to the Ginzburg-Landau system for thin films. Zbl 0976.34027
Aftalion, Amandine; Troy, William C.
2000
A singular perturbation problem arising from the Kuramoto-Sivashinski equation. Zbl 0879.34028
Raghavan, S. V.; McLeod, J. B.; Troy, W. C.
1997
Static spherically symmetric solutions of a Yang-Mills field coupled to a dilaton. Zbl 0840.34016
Hastings, S. P.; McLeod, J. B.; Troy, W. C.
1995
Linear stability of a solid ball in an undercooled liquid. Zbl 0832.73006
Chen, Xinfu; Jones, James; Troy, William C.
1995
A threshold phenomenon in the Field-Noyes model of the Belousov- Zhabotinskii reaction. Zbl 0381.92004
Troy, William C.
1977
On $$p$$-harmonic measures in half-spaces. Zbl 1432.35100
Llorente, José G.; Manfredi, Juan J.; Troy, William C.; Wu, Jang-Mei
2019
The role of Painleve II in predicting new liquid crystal self-assembly mechanisms. Zbl 1393.35210
Troy, William C.
2018
Uniqueness of positive ground state solutions of the logarithmic Schrödinger equation. Zbl 1348.35247
Troy, William C.
2016
Bifurcation analysis of a single-group asset flow model. Zbl 1403.91390
Merdan, H.; Caginalp, G.; Troy, W. C.
2016
Existence and exact multiplicity of phaselocked solutions of a Kuramoto model of mutually coupled oscillators. Zbl 1322.45005
Troy, William C.
2015
Asymmetric activity waves in synaptic cortical systems. Zbl 1171.92012
Pinto, David J.; Troy, William; Kneezel, Timothy
2009
Traveling waves and synchrony in an excitable large-scale neuronal network with asymmetric connections. Zbl 1166.45006
Troy, William C.
2008
Wave phenomena in neuronal networks. Zbl 1218.92025
Troy, W. C.
2008
Patterns and features of families of traveling waves in large-scale neuronal networks. Zbl 1210.34030
2007
The existence and uniqueness of bound-state solutions of a semi-linear equation. Zbl 1186.34038
Troy, W. C.
2005
Sustained spatial patterns of activity in neuronal populations without recurrent excitation. Zbl 1075.45011
Rubin, Jonathan E.; Troy, William C.
2004
PDE methods for nonlocal models. Zbl 1088.34011
Laing, Carlo R.; Troy, William C.
2003
Two-bump solutions of Amari-type models of neuronal pattern formation. Zbl 1011.92007
Laing, Carlo R.; Troy, William C.
2003
On the bifurcation curve for an elliptic system of FitzHugh-Nagumo type. Zbl 1082.35068
Sweers, Guido; Troy, William C.
2003
Stability of standing waves for some nonlinear Schrödinger equations. Zbl 1037.34022
McLeod, J. B.; Stuart, C. A.; Troy, W. C.
2003
Multiple bumps in a neuronal model of working memory. Zbl 1017.45006
Laing, Carlo R.; Troy, William C.; Gutkin, Boris; Ermentrout, G. Bard
2002
Boundary value problems in the Fanno model for turbulent compressible flow. Zbl 1007.76029
Hastings, S. P.; McLeod, J. B.; Troy, W. C.
2002
Spatial patterns. Higher order models in physics and mechanics. Zbl 1076.34515
Peletier, L. A.; Troy, W. C.
2001
Global branches of multi-bump periodic solutions of the Swift-Hohenberg equation. Zbl 0983.34032
van den Berg, G. J. B.; Peletier, L. A.; Troy, W. C.
2001
On the Opial-Olech-Beesack inequalities. Zbl 0979.26011
Troy, William C.
2001
Exact homoclinic and heteroclinic solutions of the Gray-Scott model for autocatalysis. Zbl 0965.34037
Hale, J. K.; Peletier, L. A.; Troy, W. C.
2000
Pattern formation described by the Swift-Hohenberg equation. Zbl 1058.35528
Peletier, L. A.; Troy, W. C.
2000
On the uniqueness of solutions to the Ginzburg-Landau system for thin films. Zbl 0976.34027
Aftalion, Amandine; Troy, William C.
2000
Stability and instability in the Gray-Scott model: The case of equal diffusivities. Zbl 0936.92034
Hale, J. K.; Peletier, L. A.; Troy, W. C.
1999
On the solutions of the one-dimensional Ginzburg-Landau equations for superconductivity. Zbl 0946.34023
Aftalion, Amandine; Troy, William C.
1999
There are asymmetric minimizers for the one-dimensional Ginzburg–Landau model of superconductivity. Zbl 0923.34019
Hastings, Stuart P.; Troy, William C.
1999
Periodic phases in second-order materials. Zbl 0931.74006
Mizel, V. J.; Peletier, L. A.; Troy, W. C.
1998
Multibump periodic travelling waves in suspension bridges. Zbl 0909.35143
Peletier, L. A.; Troy, W. C.
1998
Pulse-like spatial patterns described by higher-order model equations. Zbl 0920.34048
Peletier, L. A.; Rotariu-Bruma, A. I.; Troy, W. C.
1998
Spatial patterns described by the extended Fisher-Kolmogorov equation: Periodic solutions. Zbl 0891.34048
Peletier, L. A.; Troy, W. C.
1997
A singular perturbation problem arising from the Kuramoto-Sivashinski equation. Zbl 0879.34028
Raghavan, S. V.; McLeod, J. B.; Troy, W. C.
1997
Chaotic spatial patterns described by the extended Fisher-Kolmogorov equation. Zbl 0862.34012
Peletier, L. A.; Troy, W. C.
1996
Spatial patterns in higher order phase transitions. Zbl 0872.34032
Peletier, L. A.; Troy, W. C.
1996
A shooting approach to chaos in the Lorenz equations. Zbl 0849.34031
Hastings, S. P.; Troy, W. C.
1996
The existence of multiple solutions for a Ginzburg-Landau type model of superconductivity. Zbl 0880.34023
Hastings, S. P.; Kwong, M. K.; Troy, W. C.
1996
Stationary solutions of a fourth order nonlinear diffusion equation. Zbl 0856.35029
Peletier, L. A.; Troy, W. C.; van der Vorst, R. C. A. M.
1995
A topological shooting method and the existence of kinks of the extended Fisher-Kolmogorov equation. Zbl 0862.34030
Peletier, L. A.; Troy, W. C.
1995
Spatial patterns described by the extended Fisher-Kolmogorov (EFK) equation: Kinks. Zbl 0826.34056
Peletier, L. A.; Troy, W. C.
1995
Static spherically symmetric solutions of a Yang-Mills field coupled to a dilaton. Zbl 0840.34016
Hastings, S. P.; McLeod, J. B.; Troy, W. C.
1995
Linear stability of a solid ball in an undercooled liquid. Zbl 0832.73006
Chen, Xinfu; Jones, James; Troy, William C.
1995
The existence of spiral waves in an oscillatory reaction-diffusion system. Zbl 0823.92003
Paullet, Joseph; Ermentrout, Bard; Troy, William
1994
A computer proof that the Lorenz equations have “chaotic” solutions. Zbl 0792.65050
Hassard, B.; Zhang, J.; Hastings, S. P.; Troy, W. C.
1994
A proof that the Lorenz equations have a homoclinic orbit. Zbl 0807.34059
Hastings, S. P.; Troy, W. C.
1994
Self-similar solutions for diffusion in semiconductors. Zbl 0811.35146
Peletier, L. A.; Troy, W. C.
1994
Solutions of third-order differential equations relevant to draining and coating flows. Zbl 0807.34030
Troy, William C.
1993
On ground state solutions of $$-\Delta{} u=u^ p-u^ q$$. Zbl 0778.35039
Kwong, M. K.; McLeod, J. B.; Peletier, L. A.; Troy, W. C.
1992
A shooting approach to the Lorenz equations. Zbl 0764.58023
Hastings, S. P.; Troy, W. C.
1992
Existence of solutions to the equations governing the flow of granular materials. Zbl 0755.76012
Rajagopal, K. R.; Troy, W.; Massoudi, M.
1992
An exact reduction of Maxwell’s equations. Zbl 0797.34035
McLeod, J. B.; Stuart, C. A.; Troy, W. C.
1992
Steady solutions of the Kuramoto-Sivashinsky equation for small wave speed. Zbl 0745.34037
Jones, J.; Troy, W. C.; MacGillivary, A. D.
1992
The Skyrme model for nucleons under spherical symmetry. Zbl 0734.34023
McLeod, J. B.; Troy, W. C.
1991
Self-similar solutions for infiltration of dopant into semiconductors. Zbl 0752.35029
Peletier, L. A.; Troy, W. C.
1991
Radial solutions of $$\Delta u+f(u)=0$$ with prescribed numbers of zeros. Zbl 0695.34020
McLeod, Kevin; Troy, W. C.; Weissler, F. B.
1990
Nonexistence of monotone solutions in a model of dendritic growth. Zbl 0701.34046
Troy, William C.
1990
Bounded solutions of $$\Delta u+|u|^{p-1}u-|u|^{q-1}u=0$$ in the supercritical case. Zbl 0736.34026
Troy, William C.
1990
The existence of steady solutions of the Kuramoto-Sivashinsky equation. Zbl 0693.34053
Troy, William C.
1989
On some conjectures of Turcotte, Spence, Bau, and Holmes. Zbl 0704.34027
Hastings, S. P.; Troy, W. C.
1989
The uniqueness and stability of the rest state for strongly coupled oscillators. Zbl 0701.35019
Ermentrout, G. Bard; Troy, William C.
1989
Oscillating solutions of the Falkner-Skan for positive $$\beta$$. Zbl 0703.34044
Hastings, S. P.; Troy, W. C.
1988
Existence of solutions of the similarity equations for floating rectangular cavities and disks. Zbl 0657.76032
Lu, Chunqing; Kazarinoff, Nicholas D.; McLeod, J. Bryce; Troy, William C.
1988
On nonexistence of similarity solutions. Zbl 0673.35045
Peletier, L. A.; Troy, W. C.
1988
The behavior of solutions of a nonlinear boundary layer equation. Zbl 0652.76015
Lu, Chunqing; Troy, William C.
1988
Uniqueness of flow of a second-order fluid past a stretching sheet. Zbl 0613.76006
Troy, William C.; Overman, Edward A. II; Ermentrout, G. B.; Keener, James P.
1987
The existence of bounded solutions of a semilinear heat equation. Zbl 0655.35039
Troy, William C.
1987
Nonexistence for the Kassoy problem. Zbl 0645.34008
Bebernes, J.; Troy, W.
1987
Existence of logarithmic-type solutions to the Kapila-Kassoy problem in dimensions 3 through 9. Zbl 0648.34018
Eberly, D.; Troy, W. C.
1987
Oscillating solutions of the Falkner-Skan equation for negative $$\beta$$. Zbl 0621.76033
Hastings, S. P.; Troy, W. C.
1987
An existence theorem for the flow of a non-Newtonian fluid past an infinite porous plate. Zbl 0599.76013
Rajagopal, K. R.; Szeri, A. Z.; Troy, W.
1986
A note on non-universal deformations of nonlinear elastic layers. Zbl 0613.73036
Rajagopal, K. R.; Troy, W. C.; Wineman, A. S.
1986
Phaselocking in a reaction-diffusion system with a linear frequency gradient. Zbl 0606.92012
Ermentrout, G. B.; Troy, W. C.
1986
Oscillatory solutions of the Falkner-Skan equation. Zbl 0586.76049
Hastings, S. P.; Troy, W.
1985
Stationary wave solutions of a system of reaction-diffusion equations derived from the FitzHugh-Nagumo equations. Zbl 0543.35051
Klaasen, Gene A.; Troy, William C.
1984
Large amplitude stationary waves in an excitable lateral-inhibitory medium. Zbl 0561.92001
Ermentrout, G. B.; Hastings, S. P.; Troy, W. C.
1984
A one-variable map analysis of bursting in the Belousov-Zhabotinskii reaction. Zbl 0514.34033
Rinzel, John; Troy, William C.
1983
Symmetry properties in systems of semilinear elliptic equations. Zbl 0486.35032
Troy, William C.
1981
The stability of traveling wave front solutions of a reaction-diffusion system. Zbl 0467.35011
Klaasen, Gene A.; Troy, William C.
1981
The asymptotic behavior of solutions of a system of reaction-diffusion equations which models the Belousov-Zhabotinskii chemical reaction. Zbl 0467.35015
Klaasen, Gene A.; Troy, William C.
1981
The existence of traveling wave front solutions of a model of the Belousov-Zhabotinskii chemical reaction. Zbl 0429.34025
Troy, William C.
1980
The existence of solitary traveling wave solutions of a model of the Belousov-Zhabotinskii reaction. Zbl 0449.35091
Field, Richard J.; Troy, William C.
1979
Non-monotonic solutions of the Falkner-Skan boundary layer equation. Zbl 0423.76028
Troy, William C.
1979
The bifurcation of periodic solutions in the Hodgkin-Huxley equations. Zbl 0403.35090
Troy, William C.
1978
Oscillations in a third order differential equation modeling a nuclear reactor. Zbl 0349.34030
Troy, William C.
1977
A threshold phenomenon in the Field-Noyes model of the Belousov- Zhabotinskii reaction. Zbl 0381.92004
Troy, William C.
1977
Bifurcation phenomena in FitzHugh’s nerve conduction equations. Zbl 0329.92001
Troy, William C.
1976
Oscillation phenomena in the Hodgkin-Huxley equations. Zbl 0373.34019
Troy, William C.
1976
all top 5

#### Cited by 1,239 Authors

 28 Hayat, Tasawar 28 Troy, William C. 16 Peletier, Lambertus Adrianus 14 Wei, Juncheng 13 Momoniat, Ebrahim 12 Galaktionov, Victor Aleksandrovich 10 Vajravelu, Kuppalapalle 10 Wyller, John A. 9 Dancer, Edward Norman 9 Laing, Carlo R. 8 Ariel, P. Donald 8 Kilpatrick, Zachary P. 8 Llibre, Jaume 8 Massoudi, Mehrdad 8 Tersian, Stepan Agop 7 Asghar, Saleem 7 Hastings, Stuart P. 6 Bonheure, Denis 6 Coombes, Stephen 6 da Silva, Severino Horácio 6 Gazzola, Filippo 6 Ponosov, Arcady V. 6 Rajagopal, Kumbakonam Ramamani 6 Saanouni, Tarek 6 van den Berg, Jan Bouwe 6 Weth, Tobias 5 Abelman, Shirley 5 Agarwal, Ravi P. 5 Budd, Christopher John 5 Chen, Chaonien 5 Deng, Shengfu 5 Faye, Grégory 5 Feng, Yuqiang 5 Guo, Zongming 5 Mahomed, Fazal M. 5 McLeod, John Bryce 5 Oleynik, Anna 5 Pakdemirli, Mehmet 5 Poláčik, Peter 5 Qi, Yuanwei 5 Rottschäfer, Vivi 5 Sajid, Muhammad 5 Shi, Junping 5 Wang, Jiang 5 Wang, Mingxin 5 Winter, Matthias 4 Abel, M. Subhas 4 Ai, Shangbing 4 Bartuccelli, Michele V. 4 Bhowmik, Samir Kumar 4 Bolley, Catherine 4 Bressloff, Paul C. 4 Chaparova, Julia V. 4 Doelman, Arjen 4 Einevoll, Gaute T. 4 Ermentrout, Bard G. 4 Hai, Dang Dinh 4 Helffer, Bernard 4 Hutt, Axel 4 Khalique, Chaudry Masood 4 Moreira dos Santos, Ederson 4 Nandeppanavar, Mahantesh M. 4 Paullet, Joseph Edward 4 Touboul, Jonathan 4 Tsai, Je-Chiang 4 Valls Anglés, Cláudia 4 Wang, Zhi-Qiang 4 Yan, Shusen 4 Yurusoy, Muhammet 4 Zhang, Chengxiang 4 Zhou, Jun 3 Ali, Nasir 3 Álvarez-Caudevilla, Pablo 3 Bhakta, Mousomi 3 Bramburger, Jason J. 3 Champneys, Alan R. 3 Chen, Xinfu 3 Chossat, Pascal 3 Collot, Charles 3 Cortázar, Carmen 3 Danumjaya, Palla 3 Eberly, David H. 3 Faugeras, Olivier Paul 3 Fei, Xiangyang 3 García-Huidobro, Marta 3 Guo, Jong-Shenq 3 Han, Pigong 3 Iaia, Joseph A. 3 Jia, Yunfeng 3 Kaper, Tasso J. 3 Kühn, Christian 3 Lacey, Andrew A. 3 Leonov, Gennadiĭ Alekseevich 3 Lessard, Jean-Philippe 3 Li, Kaitai 3 Li, Wan-Tong 3 Lin, Taichia 3 Luo, Hong 3 Marcus, Moshe M. 3 Merle, Frank ...and 1,139 more Authors
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#### Cited in 203 Serials

 78 Journal of Differential Equations 57 Journal of Mathematical Analysis and Applications 56 Physica D 42 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 24 Nonlinear Analysis. Real World Applications 23 Applied Mathematics and Computation 20 Applied Mathematics Letters 19 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 18 Computers & Mathematics with Applications 15 Archive for Rational Mechanics and Analysis 15 Journal of Mathematical Biology 14 Discrete and Continuous Dynamical Systems 12 Rocky Mountain Journal of Mathematics 12 Communications in Nonlinear Science and Numerical Simulation 11 Applicable Analysis 11 Journal of Computational and Applied Mathematics 11 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 11 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 11 Journal of Dynamics and Differential Equations 11 Calculus of Variations and Partial Differential Equations 10 Chaos, Solitons and Fractals 10 Abstract and Applied Analysis 10 Nonlinear Analysis. Theory, Methods & Applications 9 Biological Cybernetics 9 Transactions of the American Mathematical Society 9 Nonlinear Dynamics 8 International Journal of Engineering Science 8 Mathematical Methods in the Applied Sciences 8 Communications in Partial Differential Equations 8 The Journal of Mathematical Neuroscience 7 Acta Mechanica 7 Proceedings of the American Mathematical Society 7 Quarterly of Applied Mathematics 7 Journal of Computational Neuroscience 6 Journal of Functional Analysis 6 European Journal of Applied Mathematics 6 Differential Equations and Dynamical Systems 6 Chaos 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Communications on Pure and Applied Analysis 6 SIAM Journal on Applied Dynamical Systems 5 Communications in Mathematical Physics 5 Journal of Engineering Mathematics 5 Nonlinearity 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 Mathematische Annalen 5 Studies in Applied Mathematics 5 Applied Mathematics and Mechanics. (English Edition) 5 Discrete and Continuous Dynamical Systems. Series B 4 International Journal for Numerical Methods in Fluids 4 Physics Letters. A 4 Applied Numerical Mathematics 4 Mathematical and Computer Modelling 4 Neural Computation 4 Japan Journal of Industrial and Applied Mathematics 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Journal of Nonlinear Science 4 Boundary Value Problems 3 Journal of Mathematical Physics 3 Journal of Statistical Physics 3 Mathematical Biosciences 3 Bulletin of Mathematical Biology 3 Chinese Annals of Mathematics. Series B 3 Neural Networks 3 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 3 SIAM Journal on Applied Mathematics 3 Continuum Mechanics and Thermodynamics 3 Applied Mathematics. Series B (English Edition) 3 NoDEA. Nonlinear Differential Equations and Applications 3 Journal of the European Mathematical Society (JEMS) 3 Journal of Applied Mathematics and Computing 3 Science China. Mathematics 3 Afrika Matematika 3 International Journal of Applied and Computational Mathematics 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal of Heat and Mass Transfer 2 Indian Journal of Pure & Applied Mathematics 2 Ukrainian Mathematical Journal 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Archiv der Mathematik 2 Meccanica 2 Ricerche di Matematica 2 Acta Mathematicae Applicatae Sinica. English Series 2 Japan Journal of Applied Mathematics 2 Numerical Methods for Partial Differential Equations 2 Dynamics and Stability of Systems 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 International Journal of Computer Mathematics 2 Journal of Elasticity 2 SIAM Journal on Mathematical Analysis 2 Bulletin of the American Mathematical Society. New Series 2 Topological Methods in Nonlinear Analysis 2 Electronic Journal of Differential Equations (EJDE) 2 Journal of Difference Equations and Applications 2 Mathematical Problems in Engineering 2 Acta Mathematica Sinica. English Series 2 Communications in Contemporary Mathematics 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 Journal of Applied Mathematics ...and 103 more Serials
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#### Cited in 39 Fields

 480 Partial differential equations (35-XX) 279 Ordinary differential equations (34-XX) 165 Biology and other natural sciences (92-XX) 132 Fluid mechanics (76-XX) 107 Dynamical systems and ergodic theory (37-XX) 76 Numerical analysis (65-XX) 46 Operator theory (47-XX) 43 Integral equations (45-XX) 36 Classical thermodynamics, heat transfer (80-XX) 33 Mechanics of deformable solids (74-XX) 32 Global analysis, analysis on manifolds (58-XX) 27 Statistical mechanics, structure of matter (82-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 13 Systems theory; control (93-XX) 11 Functional analysis (46-XX) 11 Probability theory and stochastic processes (60-XX) 11 Quantum theory (81-XX) 10 Optics, electromagnetic theory (78-XX) 8 Mechanics of particles and systems (70-XX) 5 Real functions (26-XX) 5 Difference and functional equations (39-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Potential theory (31-XX) 4 Computer science (68-XX) 3 Differential geometry (53-XX) 3 Relativity and gravitational theory (83-XX) 3 Geophysics (86-XX) 3 Operations research, mathematical programming (90-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral transforms, operational calculus (44-XX) 2 Statistics (62-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Information and communication theory, circuits (94-XX)