Stancu-Dumitru, Denisa Multiplicity of solutions for anisotropic quasilinear elliptic equations with variable exponents. (English) Zbl 1205.35126 Bull. Belg. Math. Soc. - Simon Stevin 17, No. 5, 875-889 (2010). 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. Cited in 4 Documents 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 Keywords:anisotropic equation; variable exponent; weak solution; mountain-pass theorem; Ekeland’s variational principle PDFBibTeX XMLCite \textit{D. Stancu-Dumitru}, Bull. Belg. Math. Soc. - Simon Stevin 17, No. 5, 875--889 (2010; Zbl 1205.35126) Full Text: Euclid