Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (1): 151-162.

• Articles • Previous Articles     Next Articles

Existence and Multiplicity of Nontrivial Solutions for Kirchhoff-Type Problem in RN

 WEI Mei-Chun, TANG Chun-Lei**   

  1. School of Mathematics and Statistics, Southwest |University, Chongqing 400715
  • Received:2013-12-13 Revised:2014-05-06 Online:2015-02-25 Published:2015-02-25
  • Contact: TANG Chun-Lei E-mail:tangcl@swu.edu.cn

Abstract:

The existence and multiplicity of nontrivial solutions are
 obtained for the Kirchhoff-type problem
$$
\left\{
   \begin{array}{ll}
 \disp -\left(a+b\int_{{\Bbb R}^N}|\nabla u|^2 {\rm d}x\right)
\Delta {u}+{V(x)u}={f(x,u)}\qq \mbox{in}\q {\Bbb R}^N,\\
 u\in H^1({\Bbb R}^N)
   \end{array}
   \right.
$$
by using the Mountain Pass Lemma, the Fountain Theorem and the
Symmetric Mountain Pass Lemma.

Key words: Kirchhoff-type problem ,  Mountain Pass Lemma ,  Fountain Theorem ,  Symmetric Mountain Pass Lemma

CLC Number: 

  • 35J35
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