An exact estimate result for a semilinear equation with critical exponent and prescribed singularity

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• 作者：Yanbin Sang ^{syb6662004@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Critical exponent ; Singular potential ; Extremal value ; Singular nonlinearity ; Multiple solutions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：447
• 期：1
• 页码：128-153
• 全文大小：463 K

文摘

We consider the singular boundary value problem where $0<\lambda <\overline{\lambda }={(\frac{N-2}{2})}^2,0<\gamma <1,2^{⁎}=\frac{2N}{N-2}$, h(x)$h(x)$ is a given function and V(x)$V(x)$ has prescribed finitely many singular points. Our goal in this paper is to establish some existence and multiplicity results for above problem when μ∈(0,μ^⁎)$\mu \in (0,{\mu }^{⁎})$ for some μ^⁎>0${\mu }^{⁎}>0$ and obtain exact estimate for extremal value μ^⁎=μ^⁎(Ω,γ,2^⁎,h(x))>0${\mu }^{⁎}={\mu }^{⁎}(\mathrm{\Omega },\gamma ,2^{⁎},h(x))>0$ for above problem.