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 22247X16305601&_mathId=si2.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=fba70658e884612d99e39c156d66d18a">22247X16305601-si2.gif">$0<\lambda <\overline{\lambda }={(\frac{N-2}{2})}^2,0<\gamma <1,2^{⁎}=\frac{2N}{N-2}$, ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305601&_mathId=si3.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=6e62ae28db1af7f4484190039cb74745" title="Click to view the MathML source">h(x)$h(x)$ is a given function and ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305601&_mathId=si389.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=b99b25d843eb6680df846bba38f4d4f5" title="Click to view the MathML source">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 ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305601&_mathId=si5.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=7f67c2b4751677eebb928cb0dc7278a2" title="Click to view the MathML source">μ∈(0,μ^⁎)$\mu \in (0,{\mu }^{⁎})$ for some ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305601&_mathId=si6.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=e4bde463563ec471611eef99d9371c15" title="Click to view the MathML source">μ^⁎>0${\mu }^{⁎}>0$ and obtain exact estimate for extremal value ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305601&_mathId=si7.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=98029ce6b8ccaa907a2929dcd6d28d0c" title="Click to view the MathML source">μ^⁎=μ^⁎(Ω,γ,2^⁎,h(x))>0${\mu }^{⁎}={\mu }^{⁎}(\mathrm{\Omega },\gamma ,2^{⁎},h(x))>0$ for above problem.