SIGN-CHANGING SOLUTIONS FOR SCHRÖDINGER EQUATIONS WITH VANISHING AND SIGN-CHANGING POTENTIALS

doi:10.1016/S0252-9602(14)60040-0

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (3): 691-702.doi: 10.1016/S0252-9602(14)60040-0

SIGN-CHANGING SOLUTIONS FOR SCHRÖDINGER EQUATIONS WITH VANISHING AND SIGN-CHANGING POTENTIALS

吴元泽, 黄毅生, 刘增

College of Sciences, China University of Mining and Technology, Xuzhou 221116, China； Department of Mathematics, Soochow University, Suzhou 215006, China

收稿日期:2012-10-25 修回日期:2013-07-27 出版日期:2014-05-20 发布日期:2014-05-20
基金资助:
The first author is supported by the Fundamental Research Funds for the Central Universities (2014QNA67).

SIGN-CHANGING SOLUTIONS FOR SCHRÖDINGER EQUATIONS WITH VANISHING AND SIGN-CHANGING POTENTIALS

WU Yuan-Ze, HUANG Yi-Sheng, LIU Zeng

College of Sciences, China University of Mining and Technology, Xuzhou 221116, China； Department of Mathematics, Soochow University, Suzhou 215006, China

Received:2012-10-25 Revised:2013-07-27 Online:2014-05-20 Published:2014-05-20
Supported by:
The first author is supported by the Fundamental Research Funds for the Central Universities (2014QNA67).

摘要/Abstract

摘要：

In this article, we study the existence of sign-changing solutions for the following Schr¨odinger equation
−Δu + λV (x)u = K(x)|u|^p−2u x ∈R^N, u →0 as |x| →+∞,
where N ≥ 3, λ > 0 is a parameter, 2 < p < 2N/N−2 , and the potentials V (x) and K(x) satisfy some suitable conditions. By using the method based on invariant sets of the descending flow, we obtain the existence of a positive ground state solution and a ground state sign-changing solution of the above equation for small λ, which is a complement of the results obtained by Wang and Zhou in [J. Math. Phys. 52, 113704, 2011].

关键词: Variational methods, bounded state solutions, sign-changing solutions

Abstract:

Key words: Variational methods, bounded state solutions, sign-changing solutions

中图分类号:

58E05

吴元泽, 黄毅生, 刘增. SIGN-CHANGING SOLUTIONS FOR SCHRÖDINGER EQUATIONS WITH VANISHING AND SIGN-CHANGING POTENTIALS[J]. 数学物理学报(英文版), 2014, 34(3): 691-702.

WU Yuan-Ze, HUANG Yi-Sheng, LIU Zeng. SIGN-CHANGING SOLUTIONS FOR SCHRÖDINGER EQUATIONS WITH VANISHING AND SIGN-CHANGING POTENTIALS[J]. Acta mathematica scientia,Series B, 2014, 34(3): 691-702.

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SIGN-CHANGING SOLUTIONS FOR SCHRÖDINGER EQUATIONS WITH VANISHING AND SIGN-CHANGING POTENTIALS

SIGN-CHANGING SOLUTIONS FOR SCHRÖDINGER EQUATIONS WITH VANISHING AND SIGN-CHANGING POTENTIALS

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