Existence and multiplicity of positive solutions for a class of nonlinear elliptic problems

Abstract

We study the existence and multiplicity of nonnegative solutions for the nonlinear elliptic problem, -Δu + v(x)u = a(x)up + Λf(x, u) for x ∈ ω and u = 0 on ∂ω, where ω is a bounded region in RN, N > 2, 1 < p 0 and f(x,u) satisfies some suitable conditions. By extracting the Palais-Smale sequences in the Nehari manifold, it is proved that there exists Λ* such that for Λ ∈(0, Λ*), the above problem has at least two positive solutions. © TÜBİTAK.