CONICET | Buscador de Institutos y Recursos Humanos

Let Ω⊂R^{N} be a smooth bounded domain. Let p>1, and let a,b be two (possibly discontinuous and unbounded) functions with b≥0 and such that b vanishes in a nontrivial subset Ω₀ of the domain Ω. We characterize the set of λ´ s such that the Dirichlet periodic parabolic degenerate logistic equation Lu=λa(x,t)u-b(x,t)u^{p} in Ω×R has a positive solution u_{λ}. We also show that u_{λ} satisfies that λ→u_{λ} is differentiable (and increasing when a≥0) for all λ. All results remain valid for the corresponding elliptic problem.