GROUND STATES FOR KIRCHHOFF-TYPE EQUATIONS WITH CRITICAL GROWTH

被引：6

作者：

Li, Quanqing ^{[1
,2
]}

Teng, Kaimin ^{[3
]}

Wu, Xian ^{[4
]}

机构：

[1] Honghe Univ, Dept Math, Mengzi 661100, Yunnan, Peoples R China

[2] Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China

[3] Taiyuan Univ Technol, Dept Math, Taiyuan 030024, Shanxi, Peoples R China

[4] Yunnan Normal Univ, Dept Math, Kunming 650092, Yunnan, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2018年 / 17卷 / 06期

基金：

山西省青年科学基金; 中国国家自然科学基金;

关键词：

Kirchhoff-type equation; critical growth; ground state solutions; HIGH-ENERGY SOLUTIONS; POSITIVE SOLUTIONS; EXISTENCE; BEHAVIOR;

D O I：

10.3934/cpaa.2018124

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the following Kirchhoff-type equation with critical growth -(a + b integral(3)(R) vertical bar del vertical bar(2)dx)Delta u + V(x)u = lambda f(x,u) + vertical bar u vertical bar(4)u, x is an element of R-3, where a > 0, b > 0, lambda > 0 and f is a continuous superlinear but subcritical nonlinearity. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large lambda by Nehari method. Moreover, we regard b as a parameter and obtain a convergence property of the ground state solution as b SE arrow 0.

引用

页码：2623 / 2638

页数：16

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