Positive solutions for a nonconvex elliptic Dirichlet problem with superlinear response

Andrzej Nowakowski, Aleksandra Orpel

DOI: http://dx.doi.org/10.12775/TMNA.2006.007

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.

Keywords


Nonconvex elliptic Dirichlet problems; positive solutions; duality method; variational method

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