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 V(x)$V(x)$ is a continuous real function on R², F(s)$F(s)$ is the primitive of f(s)$f(s)$, 0<μ<2$0<\mu <2$ and ε   is a positive parameter. Assuming that the nonlinearity f(s)$f(s)$ has critical exponential growth in the sense of Trudinger–Moser, we establish the existence and concentration of solutions by variational methods.