Infinitely many solutions to a class of quasilinear Schr枚dinger system in

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• 作者：Caisheng Chen ^{cshengchen@hhu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Quasilinear Schrö ; dinger system ; Mountain pass lemma ; (PS)(PS) condition
• 刊名：Applied Mathematics Letters
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：52
• 期：Complete
• 页码：176-182
• 全文大小：605 K

文摘

In this work, we study the existence of multiple solutions to the quasilinear Schrödinger system of 808ae16482ef484ad59daa941de2534" title="Click to view the MathML source">k$k$ equations with 80685b920f6da6103c84c80059366e90" title="Click to view the MathML source">u_j(x)→0$u_j\left(x\right)\to 0$ as 850b00497e" title="Click to view the MathML source">|x|→∞,j=1,2,…,k$\left|x\right|\to \infty ,j=1,2,\dots ,k$, and N≥2,1<p<N,k≥2$N\ge 2,1<p<N,k\ge 2$, the potential 80ccc4ee5865730" title="Click to view the MathML source">a_j(x)$a_j\left(x\right)$ is positive and bounded in R^N${\mathbb{R}}^N$, 渭_j>0,尾_ij=尾_ji${渭}_j>0,{尾}_{ij}={尾}_{ji}$ for i≠j,j=1,…,k$i\ne j,j=1,\dots ,k$. We develop a new technique to verify the 858120f58" title="Click to view the MathML source">(PS)$\left(PS\right)$ condition and then apply a version of mountain pass lemma to prove the existence of infinitely many nonnegative solutions to the above system.