Electron. J. Diff. Equ., Vol. 2015 (2015), No. 291, pp. 1-10.

Multiple positive solutions for a Kirchhoff type problem

Wenli Zhang

Abstract:
In this article, we study the existence and multiplicity of positive solutions of a Kirchhoff type equation on a smooth bounded domain $\Omega\subset \mathbb{R}^3$, and we show that the number of positive solutions of the equation depends on the topological properties of the domain. The technique is based on Ljusternik-Schnirelmann category and Morse theory.

Submitted September 2, 2014. Published November 23, 2015.
Math Subject Classifications: September 2, 2014. Published November 23, 2015.

Key Words: Positive solutions; Kirchhoff type equation; Morse theory; Ljusternik-Schnirelmann category.

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Wenli Zhang
Department of Mathematics
Changzhi University
Shanxi 046011, China
email: ywl6133@126.com

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