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Existence and multiplicity of positive solutions for the nonlinear Schrödinger–Poisson equations

Published online by Cambridge University Press:  17 July 2013

Ching-yu Chen ,
Yueh-cheng Kuo  and
Tsung-fang Wu
Ching-yu Chen
Affiliation:
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan ([email protected])
Yueh-cheng Kuo
Affiliation:
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan ([email protected])
Tsung-fang Wu
Affiliation:
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan ([email protected])
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Abstract

We study the existence and multiplicity of positive solutions for the following nonlinear Schrödinger–Poisson equations: where 2 < p ≤ 3 or 4 ≤ p < 6, λ > 0 and Q ∈ C(ℝ3). We show that the number of positive solutions is dependent on the profile of Q(x).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 4 , August 2013 , pp. 745 - 764
Copyright
Copyright © Royal Society of Edinburgh 2013 

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