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 $N\geq 3$, $00$ 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.