DOI QR코드

DOI QR Code

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)
  • 투고 : 2014.10.11
  • 발행 : 2016.01.01

초록

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.

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참고문헌

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피인용 문헌

  1. Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations onRN vol.2016, 2016, https://doi.org/10.1155/2016/9503073