Positive solutions for a nonconvex elliptic Dirichlet problem with superlinear response
KeywordsNonconvex elliptic Dirichlet problems, positive solutions, duality method, variational method
AbstractThe 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.
How to Cite
NOWAKOWSKI, Andrzej and ORPEL, Aleksandra. Positive solutions for a nonconvex elliptic Dirichlet problem with superlinear response. Topological Methods in Nonlinear Analysis. Online. 1 March 2006. Vol. 27, no. 1, pp. 177 - 194. [Accessed 22 September 2023].
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