Existence and multiplicity of nontrivial solutions for biharmonic equations with singular weight functions

Abstract

In the paper, we study a class of biharmonic equations with singular weight functions as follows: Δ2u−βΔpu+Vλ(x)u=fxuq−2uinRN,u∈H2(RN),where N≥3,Δ2u=Δ(Δu),Δpu=div(|∇u|p−2∇u),β≥0 is a parameter, 2<p,q<2NN−2 and Vλ(x)=λa(x)−b(x) with λ>0. Under some suitable assumptions on a,b and f, we obtain the existence and multiplicity of nontrivial solutions for λ large enough. An interesting phenomenon is that we do not need the condition that weight function f is integrable or bounded on whole space RN, which can be regarded as an improvement work of Sun et al. (2017).