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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Sign-changing critical points from linking type theorems


Authors: M. Schechter and W. Zou
Journal: Trans. Amer. Math. Soc. 358 (2006), 5293-5318
MSC (2000): Primary 35J20, 35J25, 58E05
Published electronically: January 24, 2006
MathSciNet review: 2238917
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, the relationships between sign-changing critical point theorems and the linking type theorems of M. Schechter and the saddle point theorems of P. Rabinowitz are established. The abstract results are applied to the study of the existence of sign-changing solutions for the nonlinear Schrödinger equation $ -\Delta u +V(x)u = f(x, u), u \in H^1({\mathbf{R}}^N),$ where $ f(x, u)$ is a Carathéodory function. Problems of jumping or oscillating nonlinearities and of double resonance are considered.


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Additional Information

M. Schechter
Affiliation: Department of Mathematics, University of California, Irvine, California 92697-3875

W. Zou
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03852-9
PII: S 0002-9947(06)03852-9
Keywords: Sign-changing critical points, linking, jumping nonlinearities, oscillations, Schr\"{o}dinger equation, double resonance
Received by editor(s): June 9, 2003
Received by editor(s) in revised form: August 14, 2004
Published electronically: January 24, 2006
Additional Notes: The first authhor was supported by an NSF grant
The second author 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 was partially supported by NSFC10001019
Article copyright: © Copyright 2006 American Mathematical Society