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Existence of solutions for anisotropic quasilinear elliptic equations with variable exponent
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Maria-Magdalena Boureanu
Published/Copyright:
April 21, 2010
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.
Keywords.: Quasiliniar elliptic equations; existence of weak solutions; anisotropic variable exponent Sobolev spaces; mountain-pass theorem; Ekeland's principle
Received: 2009-10-17
Revised: 2010-02-19
Published Online: 2010-04-21
Published in Print: 2010-September
© de Gruyter 2010
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- The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman–Opdam theory
- β-Jacobi processes
- On Laguerre–Hahn linear functionals: the symmetric companion
- On a generalization of Kantorovich operators on simplices and hypercubes
- Existence of solutions for anisotropic quasilinear elliptic equations with variable exponent
Articles in the same Issue
- The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman–Opdam theory
- β-Jacobi processes
- On Laguerre–Hahn linear functionals: the symmetric companion
- On a generalization of Kantorovich operators on simplices and hypercubes
- Existence of solutions for anisotropic quasilinear elliptic equations with variable exponent
