Multiple positive solutions for a semilinear equation with critical exponent and prescribed singularity

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• 作者：Yaoping Chen^a ; ^b ; ^{chenyaoping0020@163.com" class="auth_mail" title="E-mail the corresponding author} ; Jianqing Chen^b ; ^{jqchen@fjnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35J20 ; 35J60
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：130
• 期：Complete
• 页码：121-137
• 全文大小：714 K

文摘

This paper is devoted to the study of a semilinear equation of the form: where ence?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X15003442&_mathId=si2.gif&_user=111111111&_pii=S0362546X15003442&_rdoc=1&_issn=0362546X&md5=23c2c4f6e6447f0720294f93fb517496" title="Click to view the MathML source">Ω⊂R^N(N≥3)en"> is an open bounded domain with smooth boundary ence?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X15003442&_mathId=si3.gif&_user=111111111&_pii=S0362546X15003442&_rdoc=1&_issn=0362546X&md5=2a8b766bb31b7def1c51281bf435cc47" title="Click to view the MathML source">∂Ωen">$\partial \Omega$, ence?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X15003442&_mathId=si4.gif&_user=111111111&_pii=S0362546X15003442&_rdoc=1&_issn=0362546X&md5=6b38e2a60899cb0a1faf6fdf84bab4ff">en">rue">μ̄=(N−22)2, ence?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X15003442&_mathId=si5.gif&_user=111111111&_pii=S0362546X15003442&_rdoc=1&_issn=0362546X&md5=c7a5e5efde0de26c05d69edea2e8189b">en">$2^{\ast }=\frac{2N}{N-2}$, ence?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X15003442&_mathId=si6.gif&_user=111111111&_pii=S0362546X15003442&_rdoc=1&_issn=0362546X&md5=0a4c5b90f6df6a818e99e0195f8f43a6" title="Click to view the MathML source">h(x)>0en">$h\left(x\right)>0$ and ence?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X15003442&_mathId=si7.gif&_user=111111111&_pii=S0362546X15003442&_rdoc=1&_issn=0362546X&md5=7b70088bddfc4907368f07157cfbc11c" title="Click to view the MathML source">V(x)en">$V\left(x\right)$ has prescribed finitely many singular points. Using variational methods, we establish some existence and multiplicity of positive solutions for the problem.