Existence of Weak Non-Negative Solutions for a Class of Nonuniformly Boundary Value Problem

Abstract

Abstract. The goal of this paper is to study the existence of non-trivial non-negative weak solution for the nonlinear elliptic equation:with Dirichlet boundary condition in a bounded domain Ω ⊂ R N , N ≥ 3, where h(x) ∈ L 1 loc (Ω), f (x, s) has asymptotically linear behavior. The solutions will be obtained in a subspace of the space H 1 0 (Ω) and the proofs rely essentially on a variation of the mountain pass theorem in [12].