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On the Nonlinear Dirichlet Problem with P(x)-Laplacian

Published online by Cambridge University Press:  17 April 2009

Marek Galewski  and
Marek Płócienniczak
Marek Galewski
Affiliation:
Faculty of Mathematics, University of Lódź, Banacha 22, 90–238 Lódź, Poland e-mail: galewski@math.uni.lodz.pl, plo@math.uni.lodz.pl
Marek Płócienniczak
Affiliation:
Faculty of Mathematics, University of Lódź, Banacha 22, 90–238 Lódź, Poland e-mail: galewski@math.uni.lodz.pl, plo@math.uni.lodz.pl
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Using a dual variational method which we develop, we show the existence and stability of solutions for a family of Dirichlet problems k = 0, 1,… in a bounded domain in ℝN and with the nonlinearity satisfying some general growth conditions. The assumptions put on v are satisfied by p(x)-Laplacian operators.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 3 , June 2007 , pp. 381 - 395
Copyright
Copyright © Australian Mathematical Society 2007

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