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Multiple positive solutions for semilinear Dirichlet problems with sign-changing weight function in infinite strip domains. (English) Zbl 1173.35498

Summary: Existence and multiplicity results to the following Dirichlet problem

-Δu+u=λf(x)|u| q-1 +h(x)|u| p-1 inΩ,u>0inΩ,u=0onΩ,

are established, where Ω=Ω ' ×, Ω ' N-1 is bounded smooth domain and N2. Here 1<q<2<p<2 * (2 * =2N N-2 if N3, 2 * = if N=2) λ is a positive real parameter, the function f, among other conditions, can possibly change sign in Ω, and the function h satisfies suitable conditions. The study is based on the comparison of energy levels on Nehari manifold.

MSC:
35J65Nonlinear boundary value problems for linear elliptic equations
35J20Second order elliptic equations, variational methods
35B20Perturbations (PDE)
35D05Existence of generalized solutions of PDE (MSC2000)