Abstract. We consider semilinear elliptic equations with nonsmooth potential and resonant at high parts of the spectrum of $\left(-\Delta,H^1_0(Z)\right )$. Asymptotically at infinity we permit double resonance of ${\partial j(z,\zeta )\over\zeta }$ between two consecutive eigenvalues. The resonance is complete in the higher part of the spectrum, incomplete in the lower part. We also permit resonance asymptotically at zero. Using a variational approach based on nonsmooth critical point theory, we prove the existence of a nontrivial solution.
AMS Subject Classification
(1991): 35J20, 35J85
Keyword(s):
Eigenvalues,
resonance,
unique continuation property,
orthogonality,
locally Lipschitz function,
Clarke subdifferential,
nonsmooth critical point theory,
nonsmooth linking theorem
Received November 24, 2003. (Registered under 5888/2009.)
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