Positive solutions for sublinear periodic parabolic problems

✍ Scribed by T. Godoy; U. Kaufmann; S. Paczka

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 153 KB
• Volume: 55
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(03)00212-8

✦ Synopsis

Let

be a bounded domain in R N . We characterize the set of positive principal eigenvalues for the Dirichlet periodic parabolic problem Lu = g(x; t; u) in × R, under the assumptions that g is a function such that → g(x; t; )= is continuously di erentiable and nonincreasing in [0; ∞) a.e. (x; t) ∈ × R satisfying some integrability and positivity conditions. We also prove the uniqueness of the positive solution. As a consequence we obtain a necessary and su cient condition for the existence of a (unique) positive solution for the periodic parabolic logistic equation with unbounded weights. Existence of positive solutions for a generalization of the logistic equation is also shown.