A Linking Type Method to Solve a Class of Semilinear Elliptic Variational Inequalities

The aim of this paper is to study the existence of a nontrivial solution of the following semilinear elliptic variational inequality where Ω is an open bounded subset of ℝ (N ≥ 1), λ is a real parameter, with ≥ λ the first eigenvalue of the operator Δ in H (Ω), ψ belongs to H (Ω), ψ ≥ 0 and p is a C...

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Bibliographic Details
Published in:Advanced nonlinear studies 2002-02, Vol.2 (1), p.1-17
Main Authors: Matzeu, Michele, Servadei, Raffaella
Format: Article
Language:English
Subjects:
linking type critical points
nonlinearity of superlinear growth
penalization method
Semilinear variational inequalities
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Summary:The aim of this paper is to study the existence of a nontrivial solution of the following semilinear elliptic variational inequality where Ω is an open bounded subset of ℝ (N ≥ 1), λ is a real parameter, with ≥ λ the first eigenvalue of the operator Δ in H (Ω), ψ belongs to H (Ω), ψ ≥ 0 and p is a Carathéodory function on Ω × ℝ, which satisfies some general superlinearity growth conditions at zero and at infinity.
ISSN:1536-1365
2169-0375
DOI:10.1515/ans-2002-0101