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چکیده
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This paper deals with the existence and multiplicity of nontrivial weak solutions for the following equation involving variable exponents: − △p(x) u + |u| r−2u |x| r = λh(x, u), in Ω, u = 0, on ∂Ω, where Ω is a bounded domain of R N with smooth enough boundary which is subject to Dirichlet boundary condition. Using a variational method and Krasnoselskii’s genus theory, we would show the existence and multiplicity of the solutions. Next, we study closedness of set of eigenfunctions, such that p(x) ≡ p.
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