## Sign-changing critical points from linking type theorems

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- by M. Schechter and W. Zou PDF
- Trans. Amer. Math. Soc.
**358**(2006), 5293-5318 Request permission

## 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.## References

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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
- MR Author ID: 366305
- 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 - © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**358**(2006), 5293-5318 - MSC (2000): Primary 35J20, 35J25, 58E05
- DOI: https://doi.org/10.1090/S0002-9947-06-03852-9
- MathSciNet review: 2238917