Abstract
We establish the existence and multiplicity of solutions for a class of quasilinear elliptic equations involving the anisotropic \({\vec{p}(\cdot)}\)-Laplace operator, on a bounded domain with smooth boundary. We work on the weighted anisotropic variable exponent Sobolev space and our main tools are Sobolev embeddings and the mountain pass theorem.
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Rădulescu, V.D., Stăncuţ, IL. Combined concave–convex effects in anisotropic elliptic equations with variable exponent. Nonlinear Differ. Equ. Appl. 22, 391–410 (2015). https://doi.org/10.1007/s00030-014-0288-8
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DOI: https://doi.org/10.1007/s00030-014-0288-8