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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 4, 2001, pp. 845–857
DOI: 10.4171/ZAA/1048

Published online: 2001-12-31

Existence and Regularity Results for Non-Negative Solutions of some Semilinear Elliptic Variational Inequalities via Mountain Pass Techniques

Mario Girardi, Loretta Mastroeni[1] and Michele Matzeu[2]

(1) Università degli Studi di Roma Tre, Italy
(2) Università di Roma Tor Vergata, Italy

The main result stated in the present paper is the existence of a non-negative solution for a semilinear variational inequality through the use of some estimates for the Mountain-Pass critical points obtained for the penalized equations associated with the variational inequality. The positivity of the solution is achieved through a regularity result and the strong maximum principle.

Keywords: Semilinear variational inequalities, penalization method, Mountain-Pass theorem

Girardi Mario, Mastroeni Loretta, Matzeu Michele: Existence and Regularity Results for Non-Negative Solutions of some Semilinear Elliptic Variational Inequalities via Mountain Pass Techniques. Z. Anal. Anwend. 20 (2001), 845-857. doi: 10.4171/ZAA/1048