Extremal equilibria for reaction-diffusion equations in bounded domains and applications

Journal of Differential Equations

Volumn 244, Issue 12, 2008, Pages 2983-3030

  Rodríguez Bernal, Aníbal ^a   Vidal López, Alejandro ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 42649125985     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2008.02.046     Document Type: Article

References (25)

1. Amann H. Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18 4 (1976) 620-709
2. Amann H. Nonlinear operators in ordered Banach spaces and some applications to nonlinear boundary value problems. Nonlinear Operators and the Calculus of Variations. Summer School, Univ. Libre Bruxelles, Brussels, 1975. Lecture Notes in Math. vol. 543 (1976), Springer-Verlag, Berlin 1-55
3. Amann H. Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. Function Spaces, Differential Operators and Nonlinear Analysis. Friedrichroda, 1992. Teubner-Texte Math. vol. 133 (1993), Teubner, Stuttgart 9-126
4. Amann H. Linear and Quasilinear Parabolic Problems, vol. I. Monogr. Math. vol. 89 (1995), Birkhäuser, Boston, MA abstract linear theory
5. Arrieta J.M., Carvalho A.N., and Rodríguez-Bernal A. Attractors of parabolic problems with nonlinear boundary conditions. Uniform bounds. Comm. Partial Differential Equations 25 1-2 (2000) 1-37
6. Arrieta J.M., Cholewa J.W., Dlotko T., and Rodríguez-Bernal A. Asymptotic behavior and attractors for reaction diffusion equations in unbounded domains. Nonlinear Anal. 56 4 (2004) 515-554
7. Berestycki H., and Lions P.-L. Some applications of the method of super and subsolutions. Bifurcation and Nonlinear Eigenvalue Problems, Proc., Session. Univ. Paris XIII, Villetaneuse, 1978. Lecture Notes in Math. vol. 782 (1980), Springer-Verlag, Berlin 16-41
8. Berestycki H., Nirenberg L., and Varadhan S.R.S. The principal eigenvalue and maximum principle for second-order elliptic operators in general domains. Comm. Pure Appl. Math. 47 1 (1994) 47-92
9. Brézis H., and Oswald L. Remarks on sublinear elliptic equations. Nonlinear Anal. TMA 10 (1986) 55-64
10. Cazenave T., and Haraux A. Introduction aux problèmes d'évolution semi-linéaires (1990), Ellipses
11. Daners D., and Koch-Medina P. Abstract Evolution Equations, Periodic Problems and Applications. Pitman Res. Notes Math. Ser. vol. 279 (1992), Longman Scientific & Technical, Harlow
12. de Figueiredo D.G. Positive solutions of semilinear elliptic problems. Differential Equations. São Paulo, 1981. Lecture Notes in Math. vol. 957 (1982), Springer-Verlag, Berlin 34-87
13. Fraile J.M., Koch-Medina P., López-Gómez J., and Merino S. Elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equation. J. Differential Equations 127 1 (1996) 295-319
14. Hale J.K. Asymptotic Behavior of Dissipative Systems. Math. Surveys Monogr. vol. 25 (1988), Amer. Math. Soc., Providence, RI
15. Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math. vol. 840 (1981), Springer-Verlag
16. Hernández J. Positive solutions for the logistic equation with unbounded weights. Reaction Diffusion Systems. Trieste, 1995. Lect. Notes Pure Appl. Math. vol. 194 (1998), Dekker, New York 183-197
17. Lions P.L. On the existence of positive solutions of semilinear elliptic equations. SIAM Rev. 24 4 (1982) 441-467
18. López-Gómez J. The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems. J. Differential Equations 127 1 (1996) 263-294
19. Lunardi A. Analytic Semigroups and Optimal Regularity in Parabolic Problems. Progr. Nonlinear Differential Equations Appl. vol. 16 (1995), Birkhäuser, Basel
20. k spaces. Trans. Amer. Math. Soc. 278 1 (1983) 21-55
21. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations (1983), Springer-Verlag, New York
22. Rodríguez-Bernal A., and Vidal-López A. Extremal equilibria and asymptotic behavior of parabolic nonlinear reaction-diffusion equations. Nonlinear Elliptic and Parabolic Problems. Progr. Nonlinear Differential Equations Appl. vol. 64 (2005), Birkhäuser, Basel 509-516
23. Rodríguez-Bernal A., and Vidal-López A. Extremal equilibria for parabolic non-linear reaction-diffusion equations. Proceedings of Equadiff 11 (2007) 531-539
24. Sattinger D.H. Monotone methods in nonlinear elliptic and parabolic boundary value problems. Indiana Univ. Math. J. 21 (1971/72) 979-1000
25. Smith H.L. Monotone Dynamical Systems. Math. Surveys Monogr. vol. 41 (1995), Amer. Math. Soc., Providence, RI