A multiplicity result for a class ofnonlinear variational inequalities

Authors

Abstract

We consider a class of variational inequalities and we give an existence result of a nonnegative, not identically zero solution. Such result generalizes the ones in [4] and [9], which were obtained by topological methods, to nonlinear variational inequalities. We also obtain the existence of at least two not identically zero solutions for a class of semilinear elliptic variational inequalities which have been studied in [4] and [9]. Our proof of the existence result is based on the so called direct method, i.e., we introduce a suitable functional and we prove that it has a minimum, which is a solution of the variational inequality. The proof of the multiplicity result follows from [4], [9] and suitable functional estimates.

Published

2005-02-01

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Section

Articles

How to Cite

A multiplicity result for a class ofnonlinear variational inequalities. (2005). Nonlinear Studies, 12(1). https://nonlinearstudies.com/index.php/nonlinear/article/view/214