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On the Existence of Nontrivial Solutions to Some Elliptic Variational Inequalities

Abstract The paper is concerned with the existence of nontrivial solutions of the obstacle problem: where K = {υ ∈ H10(Ω) : υ ≤ ψ a.e. on Ω}. By using a generalized mountain pass theorem for inequalities, we prove, subject to some restrictions on the obstacle ψ, the existence of nontrivial solutions of the above inequality.