一类超线性(p,2)-拉普拉斯Dirichlet问题的非平凡解

数学物理学报 ›› 2017, Vol. 37 ›› Issue (1): 92-101.

一类超线性(p,2)-拉普拉斯Dirichlet问题的非平凡解

裴瑞昌¹, 张吉慧², 马草川¹

1. 天水师范学院数学与统计学院甘肃天水 741001;
2. 南京师范大学数学科学学院南京 210097

收稿日期:2016-03-09 修回日期:2016-10-27 出版日期:2017-02-26 发布日期:2017-02-26
作者简介:裴瑞昌,E-mail:prc211@163.com
基金资助:
国家自然科学基金（11661070，11571176）、甘肃省自然科学基金（1506RJZE114，1606RJYE237）和甘肃省高等学校科研基金（2015A-129，2015A-131）

Nontrivial Solutions for a Class of Superlinear (p, 2)-Laplacian Dirichlet Problems

Pei Ruichang¹, Zhang Jihui², Ma Caochuan¹

1. School of Mathematics and Statistics, Tianshui Normal University, Gansu Tianshui 741001;
2. Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097

Received:2016-03-09 Revised:2016-10-27 Online:2017-02-26 Published:2017-02-26
Supported by:
Supported by the NSFC (11661070, 11571176), the Natural Science Foundation of Gansu Province (1506RJZE114, 1606RJYE237) and the Scientific Research Foundation of the Higher Education Institutions of Gansu Province (2015A-129, 2015A-131)

摘要/Abstract

摘要：

该文研究了一类特殊的（p，2）-拉普拉斯Dirichlet问题，非线性项在无穷远处是超线性但不满足Ambrosetti-Rabinowitz条件.当2 < p < N时，利用Morse理论建立了一些一般情形下非平凡解的存在性结果.当p=N时，利用Morse理论与Moser-Trudinger不等式得到了类似的结论.

关键词: (p, 2)-拉普拉斯Dirichlet问题, Morse理论, 次临界指数型增长, 改进型次临界多项式增长

Abstract:

In this paper, we consider a class of particular (p,2)-Laplacian Dirichlet problem with nonlinearity which is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition at infinity. Some existence results for nontrivial solution are established by Morse theory in the general case 2 < p < N and similar results are also established by combining Morse theory with Moser-Trudinger inequality when p=N.

Key words: (p,2)-Laplacian Dirichlet problem, Morse theory, Subcritical exponential growth, Improved subcritical polynomial growth

中图分类号:

O175.23

裴瑞昌, 张吉慧, 马草川. 一类超线性(p,2)-拉普拉斯Dirichlet问题的非平凡解[J]. 数学物理学报, 2017, 37(1): 92-101.

Pei Ruichang, Zhang Jihui, Ma Caochuan. Nontrivial Solutions for a Class of Superlinear (p, 2)-Laplacian Dirichlet Problems[J]. Acta mathematica scientia,Series A, 2017, 37(1): 92-101.

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