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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 15
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Research Article

Multiple positive solutions for a class of Kirchhoff equation on bounded domain

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ABSTRACT

In this paper, we study the existence of multiple positive solutions of the following Kirchhoff equation {(a+bΩ|u|2dx)Δu+λu=|u|pϵ2u,inΩ,u=0,inR3Ω,u>0,inΩ,where ϵ>0, Ω is a regular bounded domain of R3, λ0, a,b>0, pϵ:=6ϵ>4. We obtain the existence of catΩ(Ω)+1 positive solutions by using the variational methods and Lusternik–Schnirelmann theory.

2010 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China (NNSFC) [11671077].

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