Boureanu, Maria-Magdalena Existence of solutions for an elliptic equation involving the \(p(x)\)-Laplace operator. (English) Zbl 1128.35331 Electron. J. Differ. Equ. 2006, Paper No. 97, 10 p. (2006). Summary: In this paper we study an elliptic equation involving the \(p(x)\)-Laplace operator on the whole space \(\mathbb{R}^N\). For that equation we prove the existence of a nontrivial weak solution using as main argument the mountain pass theorem of A. Ambrosetti and P. H. Rabinowitz [J. Funct. Anal. 14, 349–381 (1973; Zbl 0273.49063)]. Cited in 3 Documents MSC: 35J60 Nonlinear elliptic equations 35J20 Variational methods for second-order elliptic equations 35D05 Existence of generalized solutions of PDE (MSC2000) Keywords:\(p(x)\)-Laplace operator; Sobolev space with variable exponent; mountain pass theorem; weak solution Citations:Zbl 0273.49063 PDFBibTeX XMLCite \textit{M.-M. Boureanu}, Electron. J. Differ. Equ. 2006, Paper No. 97, 10 p. (2006; Zbl 1128.35331) Full Text: EuDML EMIS