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Existence of solutions for an elliptic equation involving the \(p(x)\)-Laplace operator. (English) Zbl 1128.35331

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)].

MSC:

35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
35D05 Existence of generalized solutions of PDE (MSC2000)

Citations:

Zbl 0273.49063
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