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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.

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