Electron. J. Diff. Equ., Vol. 2013 (2013), No. 98, pp. 1-8.

Infinitely many solutions for sublinear Kirchhoff equations in R^N with sign-changing potentials

Anouar Bahrouni

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 $K(x), V(x)$, 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.

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Anouar Bahrouni
Mathematics Department, University of Monastir
Faculty of Sciences, 5019 Monastir, Tunisia
email: bahrounianouar@yahoo.fr, Fax + 216 73 500 278

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