Existence Results for an Elliptic Equation of Kirchhoff-Type with Changing Sign Data

Abstract

Let Ω be a bounded domain in R^N (N > 2). We are concerned with the existence and nonexistence of solutions for the following nonlocal problem, –M (∫_Ω|∇u(x)|²dx)Δu = |u|^p–1u + λf(x) in Ω, u_|∂Ω = 0. Where M is continuous function on R⁺ and f ∈ C¹($\overline{\Omega}$) changes sign. λ and p are positive parameters. By direct variational method, Galerkin approach and sub and super solutions method some results are established.