Existence and concentration of positive ground states for a 1-Laplacian problem in RN
Existence and concentration of positive ground states for a 1-Laplacian problem in RN
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DOI：
10.1016/j.aml.2019.106045
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发表时间：
2020-02
期刊：
影响因子：
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通讯作者：
Guofeng Che;Hongxia Shi;Zewei Wang
中科院分区：
文献类型：
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作者：
Guofeng Che;Hongxia Shi;Zewei Wang
本文讨论如下拟线性椭圆型问题：−εΔ1u+V(X)u|u|=K(X)|u|p−1u，在RN中，u∈BV(RN)，其中0<；p<；1N−1，N≥2，ε>；0为小参数。在非负函数V(X)和K(X)的一些较温和的条件下，我们证明了上述问题的基态解uε的存在性。此外，uε集中于V(X)的全局最小点与K(X)的最大点的交集。该方法基于Nehari流形技术和狮子群的集中紧凑原理。
This paper is concerned with the following quasilinear elliptic problem:− ε Δ 1 u+ V (x) u| u|= K (x)| u| p− 1 u, in R N, u∈ B V (R N), where 0< p< 1 N− 1, N≥ 2 and ε> 0 is a small parameter. Under some mild conditions on the nonnegative functions V (x) and K (x), we establish the existence of a ground state solution u ε for the above problem. Moreover, u ε concentrates on the intersection set of global minimum points of V (x) and maximum points of K (x). The methods are based on the Nehari manifold technique and the Concentration-Compactness Principle of Lions.