带Sobolev临界指数的超线性Kirchhoff型方程正解的存在性与多解性

数学物理学报 ›› 2017, Vol. 37 ›› Issue (6): 1119-1124.

带Sobolev临界指数的超线性Kirchhoff型方程正解的存在性与多解性

廖家锋^1,2, 李红英¹

1 西华师范大学数学与信息学院四川南充 637002;
2 遵义师范学院数学学院贵州遵义 563002

收稿日期:2016-09-13 修回日期:2017-04-15 出版日期:2017-12-26 发布日期:2017-12-26
作者简介:廖家锋,E-mail:liaojiafeng@163.com;李红英,E-mail:lihongyingnch@163.com
基金资助:
国家自然科学基金（11471267）、贵州省教育厅自然科学基金（KY[2016]046）和西华师范大学博士启动基金（16E014）

Existence and Multiplicity of Positive Solutions for the Superlinear Kirchhoff-Type Equations with Critical Sobolev Exponent

Liao Jiafeng^1,2, Li Hongying¹

1 School of Mathematics and Information, China West Normal University, Sichuan Nanchong 637002;
2 College of Mathematical Sciences, Zunyi Normal College, Guizhou Zunyi 563002

Received:2016-09-13 Revised:2017-04-15 Online:2017-12-26 Published:2017-12-26
Supported by:
Supported by the NSFC (11471267), the Natural Science Foundation of Education of Guizhou Province (KY[2016]046) and the Doctoral Scientific Research Foundation of China West Normal University (16E014)

摘要/Abstract

摘要： 该文研究了一类带Sobolev临界指数的超线性Kirchhoff型问题，利用变分方法获得了该问题正解的存在性以及多解性.同时获得了一个关于该问题的全局（PS）条件.

关键词: Kirchhoff型方程, 临界指数, 正解, 变分方法, (PS)条件

Abstract: In this paper, we consider a class of superlinear Kirchhoff-type problems with Sobolev critical exponent. Using the variational method, we obtain the existence and multiplicity of positive solutions. Moreover, a global (PS) condition is obtained for this critical problem.

Key words: Kirchhoff-type equation, Critical exponent, Positive solutions, Variational method, (PS) condition

中图分类号:

O175.25

廖家锋, 李红英. 带Sobolev临界指数的超线性Kirchhoff型方程正解的存在性与多解性[J]. 数学物理学报, 2017, 37(6): 1119-1124.

Liao Jiafeng, Li Hongying. Existence and Multiplicity of Positive Solutions for the Superlinear Kirchhoff-Type Equations with Critical Sobolev Exponent[J]. Acta mathematica scientia,Series A, 2017, 37(6): 1119-1124.

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