Multiplicity results for p(x)-biharmonic equations with nonlinear boundary conditions

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In this paper, we are interested in the existence of multiple weak solutions of the following fourth-order nonlinear elliptic problem with a -biharmonic operator where is a bounded domain, is the operator of fourth order called the -biharmonic operator, and , are non-negative weight functions with compact support in Ω. Our analysis mainly relies on variational arguments and some recent theory on the generalized Lebesgue–Sobolev spaces and .