Infinitely many sign-changing solutions for a Schrödinger equation in R

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• 作者：Mingli Hong
• 关键词：Schrö ; dinger equations ; Invariant sets ; Multiple solutions ; Sign-changing solutions ; Fountain Theorem
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2009
• 出版时间：15 June 2009
• 年：2009
• 卷：354
• 期：2
• 页码：459-468
• 全文大小：198 K

文摘

In this paper, we consider a Schrödinger equation −Δu+(λa(x)+1)u=f(u). Applying Principle of Symmetric Criticality and the invariant set method, under some assumptions on a and f, we obtain an unbounded sequence of radial sign-changing solutions for the above equation in R^N when λ>0 large enough. As N=4 or N6, λ>0 given, using Fountain Theorem and the Principle of Symmetric Criticality, we prove that there exists an unbounded sequence of non-radial sign-changing solutions for the above equation in R^N.