Stability and attractivity of periodic solutions of parabolic systems with time delays

Journal of Mathematical Analysis and Applications

Volumn 304, Issue 2, 2005, Pages 423-450

  Pao, C V ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Asymptotic stability; Global attractivity; Lotka Volterra diffusion models; Parabolic boundary problem; Periodic solution; Quasimonotone function; Time delays; Upper and lower solutions

Indexed keywords

EID: 14844288896     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.09.014     Document Type: Article

References (35)

1. S. Ahmad A.C. Lazer Asymptotic behavior of solutions of periodic competition diffusion systems Nonlinear Anal. 13 1989 263-283
2. H. Amann Periodic solutions of semilinear parabolic equations in: Nonlinear Analysis 1978 Academic Press New York 1-29
3. D.W. Bange Periodic solutions of a quasilinear parabolic differential equation J. Differential Equations 17 1975 61-72
4. K.J. Brown P. Hess Positive periodic solutions of predator-prey reaction-diffusion systems Nonlinear Anal. 16 1991 1147-1158
5. Y. Du Positive periodic solutions of a competitor-competitor-mutualist model Differential Integral Equations 19 1996 1043-1066
6. W. Feng X. Lu Asymptotic periodicity in logistic equations with discrete delays Nonlinear Anal. 26 1996 171-178
7. P. Five Solutions of parabolic boundary problems existing for all times Arch. Rational Mech. Anal. 16 1964 155-186
8. S. Fu R. Ma Existence of a global coexistence state for periodic competition diffusion systems Nonlinear Anal. 28 1997 1265-1271
9. P. Hess Periodic-Parabolic Boundary Value Problems and Positivity Pitman Research Notes in Mathematics vol. 247 1991 Longman Scientific and Technical New York
10. Ju.S. Kolesov Periodic solutions of quasilinear parabolic equations of second order Trans. Moscow Math. Soc. 21 1970 114-146
11. A.W. Leung Systems of Nonlinear Partial Differential Equations 1989 Kluwer Academic Dordrecht
12. A.W. Leung L.A. Ortega Existence and monotone scheme for time-periodic nonquasimonotone reaction-diffusion systems: Application to autocatalytic chemistry J. Math. Anal. Appl. 221 1998 712-733
13. G.M. Lieberman Time-periodic solutions of quasilinear parabolic equations J. Math. Anal. Appl. 264 2001 617-638
14. B.P. Liu C.V. Pao Periodic solutions of coupled semilinear parabolic boundary value problems Nonlinear Anal. 6 1982 237-252
15. X. Lu W. Feng Periodic solution and oscillation in a competition model with diffusion and distributed delay effect Nonlinear Anal. 27 1996 699-709
16. M.N. Nkashama Semilinear periodic-parabolic equations with nonlinear boundary conditions J. Differential Equations 130 1996 377-405
17. C.V. Pao Nonlinear Parabolic and Elliptic Equations 1992 Plenum New York
18. C.V. Pao Periodic solutions of parabolic systems with nonlinear boundary conditions J. Math. Anal. Appl. 234 1999 695-716
19. C.V. Pao Periodic solutions of parabolic systems with time delays J. Math. Anal. Appl. 251 2000 251-263
20. C.V. Pao Coupled nonlinear parabolic systems with time delays J. Math. Anal. Appl. 196 1995 237-265
21. C.V. Pao Dynamics of nonlinear parabolic systems with time delays J. Math. Anal. Appl. 198 1996 751-779
22. C.V. Pao Quasisolutions and global attractor of reaction-diffusion systems Nonlinear Anal. 26 1996 1889-1903
23. C.V. Pao Numerical methods for time-periodic solutions of nonlinear parabolic boundary value problems SIAM J. Numer. Anal. 39 2001 647-667
24. S.G. Ruan X.Q. Zhao Persistence and extinction in two species reaction diffusion systems with delays J. Differential Equations 156 1999 71-92
25. Y. Takeuchi Global Dynamical Properties of Lotka-Volterra Systems 1996 World Scientific Singapore
26. Z. Teng Some new results of nonautonomous Lotka-Volterra competitive systems with delays J. Math. Anal. Appl. 241 2000 254-275
27. A. Tineo Existence of global coexistence for periodic competition diffusion systems Nonlinear Anal. 19 1992 335-344
28. A. Tineo J. Rivero Permanence and asymptotic stability for competition Lotka-Volterra systems with diffusion Nonlinear Anal. (RWA) 4 2003 625-637
29. L.Y. Tsai Periodic solutions of nonlinear partial differential equations Bull. Inst. Math. Acad. Sinica 5 1977 219-247
30. Y. Wang Convergence to periodic solutions in periodic quasimonotone reaction diffusion systems J. Math. Anal. Appl. 268 2002 25-40
31. J. Wu Theory and Applications of Partial Functional Differential Equations 1996 Springer-Verlag New York
32. X.Q. Zhao Global asymptotic behavior in a periodic competitor-competitor-mutualist system Nonlinear Anal. 29 1997 551-568
33. X.Q. Zhao V. Hutson Permanence in Kolmogorov periodic predator-prey models with diffusion Nonlinear Anal. 23 1994 651-668
34. S. Zheng A reaction-diffusion system of a competitor-competitor-mutualist model J. Math. Anal. Appl. 124 1987 254-280
35. L. Zhou Y.P. Fu Periodic quasimonotone global attractor of nonlinear parabolic systems with discrete delays J. Math. Anal. Appl. 250 2000 139-161