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{1,2}) are the partial generalized gradients in the sense of Clarke. Under various growth conditions on the nonlinearity 
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doi:10.1016/j.na.2004.11.012 
Copyright © 2004 Elsevier Ltd All rights reserved.
A multiplicity result for semilinear resonant elliptic problems with nonsmooth potential
Received 21 January 2004;
accepted 17 November 2004.
Available online 25 January 2005.
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Abstract
We study a semilinear elliptic problem with a nonsmooth potential and resonance at the origin between two successive eigenvalues of . Our approach is variational and is based on the nonsmooth critical point theory for locally Lipschitz functions. We prove the existence of at least two nontrivial solutions.
Keywords: Resonance; Eigenvalues and eigenspaces of the Laplacian; Local linking; Multiple nontrivial critical points; Variational characterizations of the eigenvalues; Hemivariational inequalities; Locally Lipschitz function; Subdifferential; Nonsmooth critical point theory
MSC: 35J20; 35J85; 35R70
