New Linking Theorem and Sign-Changing Solutions

Abstract

In this paper, we study the existence of sign-changing solutions for nonlinear elliptic equations via linking methods. A general liking type theorem is given with the location of the critical point produced specified in terms of the cone structure of the space. The abstract theorem is applied to elliptic equations that have jumping nonlinearities, and may or may not be resonant with respect to Fučík spectrum.

Key Words:

• Linking
• Sign-changing
• Fučík spectrum
• Jumping nonlinearities

Acknowledgments

Zou thanks the members of the Mathematics Department of the University of California at Irvine for an appointment to their department for the years 2001–2004. He also thanks the Department of Mathematics and Statistics of Utah State University for an invitation.

The author Schechter was supported in part by a NSF grant and the author Zou was supported in part by a NSFC grant. The authors thank the referee for a careful reading of the manuscript and useful comments and suggestions.