Existence and multiplicity results for a class of quasilinear Schrodinger equations in R-N involving critical growth
Existence and multiplicity results for a class of quasilinear Schrodinger equations in R-N involving critical growth
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一类涉及临界增长的R-N拟线性薛定谔方程的存在性和多重性结果
DOI：
10.1080/17476933.2016.1257002
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发表时间：
2017
影响因子：
0.9
通讯作者：
Shi Shaoyun
中科院分区：
文献类型：
--
作者：
Song Yueqiang;Shi Shaoyun
建立了文[1]中一类拟线性薛定谔方程的多凸解的存在性，其中和h是连续函数，它们是验证某些假设的连续函数。通过变量变换，将拟线性方程化为半线性方程，其相关泛函在通常的Sobolev空间中被很好地定义，并且在适当的假设下满足山路定理的几何条件。我们证明了，如果V(X)的零集有几个孤立连通分支，使得的内部不是空的且光滑的，那么对于大的，对于任何非空子集，都存在一个陷于的邻域内的凸解。
The existence of multi-bump solutions for the following class of quasilinear Schrödinger equations in is established, where and h is a continuous function, are continuous functions verifying some hypotheses. By a change of variables, the quasilinear equations are reduced to a semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem for suitable assumptions. We show that if the zero set of V (x) has several isolated connected components such that the interior of is not empty and is smooth, then for large there exists, for any non-empty subset, a bump solution which is trapped in a neighbourhood of.