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

Title & Authors
EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR NONLINEAR SCHRÖDINGER-KIRCHHOFF-TYPE EQUATIONS
CHEN, HAIBO; LIU, HONGLIANG; XU, LIPING;

Abstract
In this paper, we consider the following $\small{Schr{\ddot{o}}dinger}$-Kirchhoff-type equations $\small{\[a+b$${\int}_{{\mathbb{R}}^N}({\mid}{\nabla}u{\mid}^2+V(x){\mid}u{\mid}^2)dx$$\}$$\small{]}$$\small{[-{\Delta}u+V(x)u}$$\small{]}$$\small{=f(x,u)}$, in $\small{{\mathbb{R}}^N}$. 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
$\small{Schr{\ddot{o}}dinger}$-Kirchhoff-type;Morse theory;critical groups;variational methods;genus;
Language
English
Cited by
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