Two solutions for a class of singular Kirchhoff‐type problems with Hardy–Sobolev critical exponent II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

Two solutions for a class of singular Kirchhoff‐type problems with Hardy–Sobolev critical exponent II

Authors:	Jia‐Feng Liao

Abstract:	In this article, we devote ourselves to investigate the following singular Kirchhoff‐type equation: $(? (Ω) open= \| ? u \|^{2} d x Δ u = \frac{u^{5 ? 2 s}}{\| x \|^{s}} + \frac{λ}{\| x \|^{β} u^{γ}}, x \in Ω, u > 0, x \in Ω, u = 0, x \in ? Ω,$ where $Ω ? ?^{3}$ is a bounded domain with smooth boundary ?Ω,0∈Ω,a≥0,b,λ>0,0<γ,s<1, and $0 \leq β < \frac{5 + γ}{2} .$ By using the variational and perturbation methods, we obtain the existence of two positive solutions, which generalizes and improves the recent results in the literature.

Keywords:	Hardy– Sobolev critical exponent Kirchhoff‐type equation perturbation method positive solution singularity