On the existence of positive solutions for periodic parabolic sublinear problems. (English) Zbl 1133.35380

Godoy, T.; Kaufmann, U.

Abstr. Appl. Anal. 2003, No. 17, 975-984 (2003).

Summary: We give necessary and sufficient conditions for the existence of positive solutions for sublinear Dirichlet periodic parabolic problems \(Lu=g(x,t,u)\) in \(\Omega\times\mathbb R\) (where \(\Omega \subset\mathbb R^N\) is a smooth bounded domain) for a wide class of Carathéodory functions \(g:\Omega\times\mathbb R\times [0,\infty)\to\mathbb R\) satisfying some integrability and positivity conditions.

MSC:

35K20	Initial-boundary value problems for second-order parabolic equations
35P05	General topics in linear spectral theory for PDEs
35B10	Periodic solutions to PDEs
35B50	Maximum principles in context of PDEs

Keywords:

Dirichlet periodic parabolic problems