Existence of positive ground state solutions for a critical Kirchhoff type problem with sign-changing potential期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Existence of positive ground state solutions for a critical Kirchhoff type problem with sign-changing potential

Authors:	Hong-Ying Li

Affiliation:	School of Mathematics and Information, China West Normal University, Nanchong 637002, People’s Republic of China

Abstract:	In this work, we are interested in studying the following Kirchhoff type problem $\{\begin{matrix} ? (a + b \int_{Ω} {\| ? u \|}^{2} d x) Δ u = f (x) {\| u \|}^{2^{1} ? 2} u + λ g (x) {\| u \|}^{q ? 1} u, & x \in Ω, \\ u = 0, & x \in ? Ω, \end{matrix} is=$ where $Ω ? R^{N} (N \geq 3)$ is a smooth bounded domain, $2^{1} = \frac{2 N}{N ? 2}$ is the critical Sobolev exponent, $0 < q < 1, λ > 0$ , and $f \in L^{\infty} (Ω)$ with the set ${x \in Ω : f (x) > 0}$ of positive measures, and $g \in L^{\infty} (Ω)$ with $g (x) \geq 0, g ? 0 .$ By the Nehari method and variational method, the existence of positive ground state solutions is obtained.

Keywords:	Kirchhoff type problem Critical exponent Positive ground state solution Nehari method Variational method
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