Generalized quasilinear asymptotically periodic Schrödinger equations with critical growth

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• 作者：Hongxia Shi ^{shihongxia5617@163.com" class="auth_mail" title="E-mail the corresponding author} ; Haibo Chen ; ^{math_chb@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Mountain Pass Theorem ; Asymptotically periodic ; Critical growth ; Concentration-compactness principle
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：71
• 期：3
• 页码：849-858
• 全文大小：381 K

文摘

This paper is concerned with the following quasilinear Schrödinger equations: where N≥3$N\ge 3$, $2^{\ast }=\frac{2N}{N-2}$, $G\left(u\right)={\int }_0^{u}g\left(t\right)dt$ and λ>0$\lambda >0$ is a parameter. By using a change of variable, the quasilinear equation is reduced to a semilinear one, whose associated functional is well defined in H¹(R^N)$H^1\left({\mathbb{R}}^N\right)$. We establish the existence of positive solutions for this problem by using the Mountain Pass Theorem in combination with the concentration-compactness principle under appropriate assumptions on V(x)$V\left(x\right)$ and f(x,u)$f(x,u)$. Recent results from the literature are improved and extended.