Abstract.
In this paper we present some existence results for a class of semilinear elliptic variational inequalities, depending on a real parameter λ, with changing sign nonlinearities. The fundamental tool to prove the existence result is a penalization method combined with the Mountain Pass Theorem and the Linking Theorem, respectively in the case λ < λ 1 and λ ≥ λ 1, where λ1 is the first eigenvalue of the uniformly elliptic operator A involved in the variational inequality.
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Servadei, R. Existence results for semilinear elliptic variational inequalities with changing sign nonlinearities. Nonlinear differ. equ. appl. 13, 311–335 (2006). https://doi.org/10.1007/s00030-006-4003-2
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DOI: https://doi.org/10.1007/s00030-006-4003-2