Multiplicity of solutions for a class of anisotropic elliptic equations with variable exponent

Abstract

We establish the existence of an unbounded sequence of solutions for a class of quasilinear elliptic equations involving the anisotropic -Laplace operator, on a bounded domain with smooth boundary. We work on the anisotropic variable exponent Sobolev spaces and our main tool is the symmetric mountain-pass theorem of Ambrosetti and Rabinowitz.

Keywords:

• quasilinear elliptic equations
• multiple weak solutions
• anisotropic variable exponent Sobolev spaces
• symmetric mountain-pass theorem

AMS Subject Classifications::

• 35J25
• 35J62
• 35D30
• 46E35
• 35J20

Acknowledgements

M.-M. Boureanu was supported by a Bitdefender Postdoctoral Fellowship at the Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy. P. Pucci was supported by the Italian MIUR project ‘Metodi Variazionali ed Equazioni Differenziali non Lineari’ and V. Rădulescu was supported by the Romanian Grant CNCSIS PNII–55/2008.