Sign--changing solutions for anasymptotically linear Schrödinger equation

Addolorata Salvatore

doi:10.3934/proc.2009.2009.669

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2009, Volume 2009: 669-677. Doi: 10.3934/proc.2009.2009.669 open access

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Sign--changing solutions for an asymptotically linear Schrödinger equation

Addolorata Salvatore^1,

1.
Dipartimento di Matematica, Università degli Studi di Bari, Via E. Orabona 4, 70125 Bari

Received: June 30, 2008

Revised: March 31, 2009

Published: August 2009

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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.

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Mathematics Subject Classification: Primary: 58E05; Secondary: 35J20, 35J60, 47J30.

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