Periodic solutions of systems of parabolic equations in unbounded domains

Nonlinear Analysis, Theory, Methods and Applications

Volumn 40, Issue 1, 2000, Pages 523-535

  Pao, C V ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; THEOREM PROVING;

PARABOLIC DIFFERENTIAL EQUATIONS; PERIODIC SOLUTIONS;

DIFFERENTIAL EQUATIONS;

EID: 0034172560     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(00)85031-2     Document Type: Article

References (21)

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, Nonlinear Analysis, Academic Press, New York, 1978, pp. 1-29.
3. D.W. Bange, Periodic solutions of a quasilinear parabolic differential equation, J. Differential Equations 17 (1975) 61-72.
4. Y. Du, Positive periodic solutions of a competitor-competitor-mutualist model, Differential Integral Equations 19 (1996) 1043-1066.
5. S. Fu, R. Ma, Existence of a global coexistence state for periodic competition diffusion systems, Nonlinear Anal. 28 (1997) 1265-1271.
6. P. Hess, Periodic-Parabolic Boundary Value Problems and Positivity, Pitman Research Notes in Mathematics, Ser. 247, Longman Scientific and Technical, New York, 1991.
7. Ju.S. Kolesov, Periodic solutions of quasilinear parabolic equations of second order, Trans. Moscow Math. Soc. 21 (1970) 114-146.
8. 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.
9. B.P. Liu, C.V. Pao, Periodic solutions of coupled scmilinear parabolic boundary value problems. Nonlinear Anal. 6 (1982) 237-252.
10. X. Lu, W. Feng, Periodic solution and oscillation in a competition model with diffusion and distributed delay effect. Nonlinear Anal. 27 (1996) 699-709.
11. J. Maginu, Stability of spatially homogeneous periodic solutions of reaction-diffusion equation, J. Differential Equations 31 (1979) 130-138.
12. M. Nakao, On boundedness, periodicity, and almost periodicity of solutions of some nonlinear parabolic equations, J. Differential Equations 19 (1975) 371-385.
13. C.V. Pao, Nonlinear Parabolic and Elliptic Equations. Plenum Press, New York, 1992.
14. C.V. Pao, Parabolic systems in unbounded domians I. Existence and dynamics, J. Math. Anal. Appl. 217 (1998) 129-160.
15. C.V. Pao, Periodic solutions of parabolic systems with nonlinear boundary condition, J. Math. Anal. Appl. 234 (1999) 695-716.
16. A. Tineo, Existence of global coexistence state for periodic competition diffusion systems. Nonlinear Anal. 19 (1992) 335-344.
17. A. Tineo, Asymptotic behavior of solutions of a periodic reaction-diffusion system of a competitor-competitor-mutualist model, J. Differential Equations 108 (1994) 326-341.
18. L.Y. Tsai. Periodic solutions of nonlinear parabolic differential equations. Bull. Inst. Math. Sinica 5 (1977) 219-247.
19. R.S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1962.
20. X.Q. Zhao, Global asymptotic behavior in a periodic competitor-competitor-mutualist system. Nonlinear Anal. 29 (1997) 551-568.
21. S. Zheng, A reaction-diffusion system of a competitor-competitor-mutualist model. J. Math. Anal. Appl. 124 (1987) 254-280.