Existence and multiplicity of solutions for a nonlocal problem with critical Sobolev exponent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 and multiplicity of solutions for a nonlocal problem with critical Sobolev exponent

Authors:	Jia-Feng Liao Hong-Ying Li Peng Zhang

Affiliation:	1. School of Mathematics and Information, China West Normal University, Nanchong, Sichuan 637002, People’s Republic of China;2. School of Mathematics and Computational Science, Zunyi Normal College, Zunyi, Guizhou 563002, People’s Republic of China

Abstract:	In this work, we are interested in considering the following nonlocal problem $\{\begin{matrix} ? (a + b \int_{Ω} {\| ? u \|}^{2} d x) Δ u = μ {\| u \|}^{2^{1} ? 2} u + λ {\| u \|}^{q ? 2} u, & x \in Ω, \\ u = 0, & x \in ? Ω, \end{matrix} is=$ where $Ω ? R^{N} (N \geq 4)$ is a smooth bounded domain, $a \geq 0, b > 0, 1 < q < 2, μ, λ > 0$ and $2^{1} = \frac{2 N}{N ? 2}$ is the critical Sobolev exponent. By using the variational method and the critical point theorem, some existence and multiplicity results are obtained.

Keywords:	Nonlocal problem Critical exponent Multiplicity Variational method The critical point theorem
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