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Multiple Nontrivial Solutions for Doubly Resonant Periodic Problems

Published:2009-12-04
Printed: Jun 2010
• Nikolaos S. Papageorgiou
• Vasile Staicu
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Abstract

We consider semilinear periodic problems with the right-hand side nonlinearity satisfying a double resonance condition between two successive eigenvalues. Using a combination of variational and degree theoretic methods, we prove the existence of at least two nontrivial solutions.
 Keywords: double resonance, generalized LL-condition, Leray-Schauder degree, Cerami condition
 MSC Classifications: 34B15 - Nonlinear boundary value problems