In this article, we study the existence and multiplicity of positive solutions of a Kirchhoff type equation on a smooth bounded domain , 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
Shanxi 046011, China
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