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

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

Abstract

Abstract:

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].

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

CLC Number:

58E05

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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