Abstract
In this article, we study the existence and multiplicity of solutions to the problem {−Δu=g(x,u), in Ω;u=0, on ∂Ω, where Ω is a bounded domain in RN(N⩾2) with smooth boundary, and g:Ω¯×R→R is a differentiable function. We will assume that g(x,s) has a resonant behavior for large negative values of s and that a Landesman–Lazer type condition is satisfied. We also assume that g(x,s) is superlinear, but subcritical, for large positive values of s. We prove the existence and multiplicity of solutions for problem (1.1) by using minimax methods and infinite-dimensional Morse theory.
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