Open Access Research

Existence of positive solutions for a critical nonlinear Schrödinger equation with vanishing or coercive potentials

Shaowei Chen

Author Affiliations

School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, P.R. China

Boundary Value Problems 2013, 2013:201  doi:10.1186/1687-2770-2013-201

Published: 8 September 2013

Abstract

In this paper we investigate the existence of positive solutions for the following nonlinear Schrödinger equation:

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where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M2">View MathML</a> and <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M3">View MathML</a> as <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M4">View MathML</a> with <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M5">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M6">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M7">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M8">View MathML</a> and <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M9','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/201/mathml/M9">View MathML</a>.

MSC: 35J20, 35J60.

Keywords:
semilinear Schrödinger equation; vanishing or coercive potentials