Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 98, pp. 1-8.

Title: Infinitely many solutions for sublinear Kirchhoff
       equations in R^N with sign-changing potentials
        
Author: Anouar Bahrouni (Univ. of Monastir, Tunisia)

Abstract:
 In this article we study the  Kirchhoff equation
 $$
  -\Big(a+b \int_{\mathbb{R}^N}|\nabla u|^2dx\Big)\Delta u+V(x)u
  = K(x)|u|^{q-1}u, \quad\hbox{in }\mathbb{R}^N,
 $$
 where $N\geq 3$, $0<q<1$, $a,b>0$ are constants and $K(x), V(x)$ both
 change sign in $\mathbb{R}^N$. Under appropriate assumptions on
 V(x), K(x), the existence of infinitely many solutions is
 proved by using the symmetric Mountain Pass Theorem.

Submitted March 6, 2013, Published April 16, 2013.
Math Subject Classifications: 35J60, 35J91, 58E30.
Key Words: Kirchhoff equations; symmetric Mountain Pass Theorem;
           infinitely many solutions.