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 science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116000109&_mathId=si2.gif&_user=111111111&_pii=S0898122116000109&_rdoc=1&_issn=08981221&md5=13113ea056a2b973cfbdcbb5c97d04c1" title="Click to view the MathML source">N≥3$N\ge 3$, science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116000109&_mathId=si3.gif&_user=111111111&_pii=S0898122116000109&_rdoc=1&_issn=08981221&md5=f19edcf964eb59b4faa907fabb187adc">$2^{\ast }=\frac{2N}{N-2}$, science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116000109&_mathId=si4.gif&_user=111111111&_pii=S0898122116000109&_rdoc=1&_issn=08981221&md5=3ceaf51bb0f98da062a5c8deafec0248">$G\left(u\right)={\int }_0^{u}g\left(t\right)dt$ and science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116000109&_mathId=si5.gif&_user=111111111&_pii=S0898122116000109&_rdoc=1&_issn=08981221&md5=6694e0b109ddedc0ca71ec166e230a79" title="Click to view the MathML source">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 science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116000109&_mathId=si6.gif&_user=111111111&_pii=S0898122116000109&_rdoc=1&_issn=08981221&md5=63e7ad1988db50e06e52ffb2418f0266" title="Click to view the MathML source">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 science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116000109&_mathId=si7.gif&_user=111111111&_pii=S0898122116000109&_rdoc=1&_issn=08981221&md5=d8e2f89e577a0e2e989d2547a780addd" title="Click to view the MathML source">V(x)$V\left(x\right)$ and science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116000109&_mathId=si8.gif&_user=111111111&_pii=S0898122116000109&_rdoc=1&_issn=08981221&md5=55e2c4140bcf6d7ea4af7fb61d08cb65" title="Click to view the MathML source">f(x,u)$f(x,u)$. Recent results from the literature are improved and extended.