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 lsi2" class="mathmlsrc">le="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305601&_mathId=si2.gif&_user=111111111&_pii=S0022247X16305601&_rdoc=1&_issn=0022247X&md5=fba70658e884612d99e39c156d66d18a">lass="imgLazyJSB inlineImage" height="20" width="306" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16305601-si2.gif">lass="mathContainer hidden">lass="mathCode">erflow="scroll">0<λ<er accent="true">λetchy="false">¯er>=etchy="false">(N−22etchy="false">)2,e width="0.25em">e>0<γ<1,e width="0.25em">e>2⁎=2NN−2, lsi3" class="mathmlsrc">lass="formulatext 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)lass="mathContainer hidden">lass="mathCode">erflow="scroll">hetchy="false">(xetchy="false">) is a given function and lsi389" class="mathmlsrc">lass="formulatext 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)lass="mathContainer hidden">lass="mathCode">erflow="scroll">Vetchy="false">(xetchy="false">) has prescribed finitely many singular points. Our goal in this paper is to establish some existence and multiplicity results for above problem when lsi5" class="mathmlsrc">lass="formulatext 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^⁎)lass="mathContainer hidden">lass="mathCode">erflow="scroll">μ∈etchy="false">(0,μ⁎etchy="false">) for some lsi6" class="mathmlsrc">lass="formulatext 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^⁎>0lass="mathContainer hidden">lass="mathCode">erflow="scroll">μ⁎>0 and obtain exact estimate for extremal value lsi7" class="mathmlsrc">lass="formulatext 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))>0lass="mathContainer hidden">lass="mathCode">erflow="scroll">μ⁎=μ⁎etchy="false">(l">Ω,γ,2⁎,hetchy="false">(xetchy="false">)etchy="false">)>0 for above problem.