Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2014.10.11
  • Published : 2016.01.01
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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

References

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