### Positive solutions for a nonconvex elliptic Dirichlet problem with superlinear response

#### 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.

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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