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.
Cite this article
Mario Girardi, Loretta Mastroeni, Michele Matzeu, Existence and Regularity Results for Non-Negative Solutions of some Semilinear Elliptic Variational Inequalities via Mountain Pass Techniques. Z. Anal. Anwend. 20 (2001), no. 4, pp. 845–857DOI 10.4171/ZAA/1048