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Existence and multiplicity of solutions of Schrödinger—Poisson systems with radial potentials

Published online by Cambridge University Press:  20 March 2014

Anran Li ,
Jiabao Su  and
Leiga Zhao
Anran Li
Affiliation:
School of Mathematical Sciences, Capital Normal University, Beijing 100048, People's Republic of China
Jiabao Su
Affiliation:
School of Mathematical Sciences, Capital Normal University, Beijing 100048, People's Republic of China
Leiga Zhao
Affiliation:
Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, People's Republic of China, (, [email protected])
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Abstract

In this paper, we deal with the nonlinear Schrödinger–Poisson system

where λ > 0, V and Q are radial functions, which can be vanishing or coercive at ∞. With assumptions on f just in a neighbourhood of the origin, existence and multiplicity of non-trivial radial solutions are obtained via variational methods. In particular, if f is sublinear and odd near the origin, we obtain infinitely many solutions of (SP)λ for any λ < 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 2 , April 2014 , pp. 319 - 332
Copyright
Copyright © Royal Society of Edinburgh 2014 

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