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http://dx.doi.org/10.4134/JKMS.2016.53.1.201

EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR NONLINEAR SCHRÖDINGER-KIRCHHOFF-TYPE EQUATIONS

CHEN, HAIBO (SCHOOL OF MATHEMATICS AND STATISTICS CENTRAL SOUTH UNIVERSITY)
LIU, HONGLIANG (SCHOOL OF MATHEMATICS AND STATISTICS CENTRAL SOUTH UNIVERSITY)
XU, LIPING (SCHOOL OF MATHEMATICS AND STATISTICS CENTRAL SOUTH UNIVERSITY)

Publication Information

Journal of the Korean Mathematical Society / v.53, no.1, 2016 , pp. 201-215 More about this Journal

Abstract

In this paper, we consider the following $Schr{\ddot{o}}dinger$ -Kirchhoff-type equations $$\[a+b${\int}_{{\mathbb{R}}^N}({\mid}{\nabla}u{\mid}^2+V(x){\mid}u{\mid}^2)dx$\$ $]$ $[-{\Delta}u+V(x)u$ $]$ $=f(x,u)$$ , in ${\mathbb{R}}^N$ . Under certain assumptions on V and f, some new criteria on the existence and multiplicity of nontrivial solutions are established by the Morse theory with local linking and the genus properties in critical point theory. Some results from the previously literature are significantly extended and complemented.

Keywords

$Schr{\ddot{o}}dinger$ -Kirchhoff-type; Morse theory; critical groups; variational methods; genus;

Citations & Related Records

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