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On the stability of solutions for the p(x)-Laplacian equation and some applications to optimisation problems with state constraints

Published online by Cambridge University Press:  17 February 2009

Elżbieta Galewska  and
Marek Galewski
Elżbieta Galewska
Affiliation:
Faculty of Mathematics, University of Lodz, Banacha 22, 90-238 Lodz, Poland; e-mail: emlynar@math.uni.lodz.pl, galewski@math.uni.lodz.pl.
Marek Galewski
Affiliation:
Faculty of Mathematics, University of Lodz, Banacha 22, 90-238 Lodz, Poland; e-mail: emlynar@math.uni.lodz.pl, galewski@math.uni.lodz.pl.
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Abstract

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We consider the stability of solutions for a family of Dirichlet problems with (p, q)-growth conditions. We apply the results obtained to show continuous dependence on a functional parameter and the existence of an optimal solution in a control problem with state constraints governed by the p(x)-Laplacian equation.

Keywords

p(x)-Laplacianstabilitycontinuous dependence on parametersoptimal solution.
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 2 , October 2006 , pp. 245 - 257
Copyright
Copyright © Australian Mathematical Society 2006

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