Existência de soluções para duas classes de problemas elípticos usando a aplicação fibração relacionada à variedade de Nehari

Abstract

The Nehari Manifold for the equation −∆u(x) = λa(x)u(x)q + b(x)u(x)p, for x ∈ Ω together with Dirichlet boundary conditions is investigated in which case a(x) = 1, λ ∈R, q = 1 and 0 < p < 1, and also in the case that λ > 0 and 0 < q < 1 < p < 2∗−1. Exploring the relationship between the Nehari manifold and fibering maps (i.e., maps of the form t → J(tu) where J is the Euler functional associated to the above equation), we will discuss the existence and multiplicity of non negative solutions.