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

ANZIAM J. 48 (2006), 245-257

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

Elzbieta Galewska
Faculty of Mathematics
University of Lodz
Banacha 22
90-238 Lodz
Poland
emlynar@math.uni.lodz.pl

and

Marek Galewski
Faculty of Mathematics
University of Lodz
Banacha 22
90-238 Lodz
Poland
galewski@math.uni.lodz.pl

Abstract

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.

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