Sign--changing solutions for an asymptotically linear Schrödinger equation

Pages: 669 - 677, Issue Special, September 2009

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Addolorata Salvatore - Dipartimento di Matematica, Università degli Studi di Bari, Via E. Orabona 4, 70125 Bari, Italy (email)

Abstract: We study an asymptotically linear Schrödinger equation in the whole Euclidean space $\mathbb{R}^N$. By using a suitable linking theorem we prove that the problem admits not only the trivial solution but also either a sign--changing solution or one positive and one negative solution.

Keywords:  Schrödinger equation, sign--changing solution, linking theorem
Mathematics Subject Classification:  Primary: 58E05; Secondary: 35J20, 35J60, 47J30

Received: July 2008;      Revised: April 2009;      Published: September 2009.