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Multiple solutions for fourth order elliptic problems with p(x)-biharmonic operators

Kong L.

Opuscula Mathematica

2016

Vol. 36, no. 2

253--264

We study the multiplicity of weak solutions to the following fourth order nonlinear elliptic problem with a p(x)-biharmonic operator [formula] where Ω is a smooth bounded domain in RN, [formula] is the p(x)-biharmonic operator, and λ > 0 is a parameter. We establish sufficient conditions under which there exists a positive number λ* such that the above problem has at least two nontrivial weak solutions for each λ > λ*. Our analysis mainly relies on variational arguments based on the mountain pass lemma and some recent theory on the generalized Lebesgue-Sobolev spaces [formula].