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- Publisher
- de Gruyter
- Copyright
- © de Gruyter 2010
- ISSN
- 1867-1152
- eISSN
- 1869-6090
- DOI
- 10.1515/APAM.2010.025
- Publisher site
- See Article on Publisher Site
Abstract
Abstract We study the existence of solutions for a class of quasilinear elliptic equations involving the anisotropic -Laplace operator, on a bounded domain with smooth boundary. Since our differential operator involves partial derivatives with different variable exponents, we work on the anisotropic variable exponent Sobolev spaces. Using the Ekeland's variational principle and the mountain-pass theorem of Ambrosetti and Rabinowitz, we establish two existence results.
Journal
Advances in Pure and Applied Mathematics – de Gruyter
Published: Sep 1, 2010
Keywords: Quasiliniar elliptic equations; existence of weak solutions; anisotropic variable exponent Sobolev spaces; mountain-pass theorem; Ekeland's principle