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On Existence and Stability of Solutions to Elliptic Systems with Generalised Growth

Published online by Cambridge University Press:  17 April 2009

Marek Galewski  and
Marek Plócienniczak
Marek Galewski
Affiliation:
Faculty of Mathematics and Computer Science, University of Lódź, Banacha 22, 90–238 Lódź, Poland, e-mail: [email protected], [email protected]
Marek Plócienniczak
Affiliation:
Faculty of Mathematics and Computer Science, University of Lódź, Banacha 22, 90–238 Lódź, Poland, e-mail: [email protected], [email protected]
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We are concerned with existence and stability of solutions for system of equations with generalised p(x) and m(x)—Laplace operators and where the nonlinearity satisfies some local growth conditions. We provide a variational approach that is based on investigation of the primal and the dual action functionals. As a consequence we consider the dependence of the the system on functional parameters.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 3 , December 2007 , pp. 453 - 470
Copyright
Copyright © Australian Mathematical Society 2007

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