Topological Methods in Nonlinear Analysis

Positive solutions for a nonconvex elliptic Dirichlet problem with superlinear response

Andrzej Nowakowski and Aleksandra Orpel

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Abstract

The existence of bounded solutions of the Dirichlet problem for a ceratin class of elliptic partial differential equations is discussed here. We use variational methods based on the subdifferential theory and the comparison principle for difergence form operators. We present duality and variational principles for this problem. As a consequences of the duality we obtain also the variational principle for minimizing sequences of $J$ which gives a measure of a duality gap between primal and dual functional for approximate solutions.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 27, Number 1 (2006), 177-194.

Dates
First available in Project Euclid: 12 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1463081852

Mathematical Reviews number (MathSciNet)
MR2236416

Zentralblatt MATH identifier
1135.35326

Citation

Nowakowski, Andrzej; Orpel, Aleksandra. Positive solutions for a nonconvex elliptic Dirichlet problem with superlinear response. Topol. Methods Nonlinear Anal. 27 (2006), no. 1, 177--194. https://projecteuclid.org/euclid.tmna/1463081852


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