Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in

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• 作者：Claudianor O. Alves^a ; ¹ ; ^{coalves@dme.ufcg.edu.br" class="auth_mail" title="E-mail the corresponding author} ; Daniele Cassani^b ; ^{daniele.cassani@uninsubria.it" class="auth_mail" title="E-mail the corresponding author} ; Cristina Tarsi^c ; ^{cristina.tarsi@unimi.it" class="auth_mail" title="E-mail the corresponding author} ; Minbo Yang^d ; ² ; ^{mbyang@zjnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35J20 ; 35J60 ; 35B33
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 August 2016
• 年：2016
• 卷：261
• 期：3
• 页码：1933-1972
• 全文大小：457 K

文摘

We study the following singularly perturbed nonlocal Schrödinger equation where class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616300559&_mathId=si102.gif&_user=111111111&_pii=S0022039616300559&_rdoc=1&_issn=00220396&md5=624c4a4f135435630643cb939a0b2f28" title="Click to view the MathML source">V(x)class="mathContainer hidden">class="mathCode">$V(x)$ is a continuous real function on class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616300559&_mathId=si1.gif&_user=111111111&_pii=S0022039616300559&_rdoc=1&_issn=00220396&md5=0ce7621b208768cb77555780a434d92e" title="Click to view the MathML source">R²class="mathContainer hidden">class="mathCode">${\mathbb{R}}^2$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616300559&_mathId=si4.gif&_user=111111111&_pii=S0022039616300559&_rdoc=1&_issn=00220396&md5=54842b191f6db5938fd11a23a9d467e3" title="Click to view the MathML source">F(s)class="mathContainer hidden">class="mathCode">$F(s)$ is the primitive of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616300559&_mathId=si100.gif&_user=111111111&_pii=S0022039616300559&_rdoc=1&_issn=00220396&md5=b645d2ec0d7fcb4191cd3e5c2564fb51" title="Click to view the MathML source">f(s)class="mathContainer hidden">class="mathCode">$f(s)$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616300559&_mathId=si6.gif&_user=111111111&_pii=S0022039616300559&_rdoc=1&_issn=00220396&md5=4a106a306794ab7c9fc490a5aad173dd" title="Click to view the MathML source">0<μ<2class="mathContainer hidden">class="mathCode">$0<\mu <2$ and ε   is a positive parameter. Assuming that the nonlinearity class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616300559&_mathId=si100.gif&_user=111111111&_pii=S0022039616300559&_rdoc=1&_issn=00220396&md5=b645d2ec0d7fcb4191cd3e5c2564fb51" title="Click to view the MathML source">f(s)class="mathContainer hidden">class="mathCode">$f(s)$ has critical exponential growth in the sense of Trudinger–Moser, we establish the existence and concentration of solutions by variational methods.