JournalsrlmVol. 25, No. 1pp. 91–108

Existence and multiplicity results for anisotropic stationary Schrödinger equations

  • Ghasem A. Afrouzi

    University of Mazandaran, Babolsar, Iran
  • Maryam Mirzapour

    University of Mazandaran, Babolsar, Iran
  • Vicenţiu D. Rădulescu

    University of Craiova, Romania
Existence and multiplicity results for anisotropic stationary Schrödinger equations cover
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Abstract

In this paper we are concerned with a new class of quasilinear elliptic equations with a power-like reaction term and a di¤erential operator that involves partial derivatives with different powers. The functional-analytic framework relies on anisotropic Sobolev spaces. By means of combined variational arguments, we obtain the existence of weak solutions and, in case of symmetric settings, the existence of large or small energy solutions. In particular, we establish some results that extend the classical theory of combined e¤ects of concave and convex nonlinearities.

Cite this article

Ghasem A. Afrouzi, Maryam Mirzapour, Vicenţiu D. Rădulescu, Existence and multiplicity results for anisotropic stationary Schrödinger equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 25 (2014), no. 1, pp. 91–108

DOI 10.4171/RLM/669