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Advances in Nonlinear Analysis

Editor-in-Chief: Radulescu, Vicentiu / Squassina, Marco

IMPACT FACTOR 2018: 6.636

CiteScore 2018: 5.03

SCImago Journal Rank (SJR) 2018: 3.215
Source Normalized Impact per Paper (SNIP) 2018: 3.225

Mathematical Citation Quotient (MCQ) 2017: 1.89

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Existence of a positive solution for nonlinear Schrödinger equations with general nonlinearity

Yohei Sato
  • Department of Mathematics, Saitama University, Shimo-Okubo 255, Sakura-ku Saitama-shi, 338-8570, Japan; and Osaka City University Advanced Mathematical Institute, 3-3-138 Sugimoto, Smiyoshi-ku, Osaka, 558-8585, Japan
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/ Masataka Shibata
Published Online: 2014-05-24 | DOI: https://doi.org/10.1515/anona-2014-0003


We study the following nonlinear Schrödinger equations: -Δu+V(x)u=f(u)inN. The purpose of this paper is to establish the existence of a positive solution under general conditions which are weaker than the Ambrosetti–Rabinowitz condition.

Keywords: Variational method; nonlinear Schrödinger equation; positive solution

MSC: 35J20; 35J61; 49J35

About the article

Received: 2014-01-16

Accepted: 2014-04-28

Published Online: 2014-05-24

Published in Print: 2014-09-01

Citation Information: Advances in Nonlinear Analysis, Volume 3, Issue S1, Pages s55–s67, ISSN (Online) 2191-950X, ISSN (Print) 2191-9496, DOI: https://doi.org/10.1515/anona-2014-0003.

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