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Multiplicity of solutions for anisotropic quasilinear elliptic equations with variable exponents. (English) Zbl 1205.35126

Summary: We study an anisotropic partial differential equation on a bounded domain \(\Omega\subset\mathbb R^N\). We prove the existence of at least two nontrivial weak solutions using as main tools the mountain pass lemma and Ekeland’s variational principle.

MSC:

35J70 Degenerate elliptic equations
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35D30 Weak solutions to PDEs
35J20 Variational methods for second-order elliptic equations
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Full Text: Euclid