一类带强制位势的p-Laplace特征值问题

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1323-1332.

一类带强制位势的p-Laplace特征值问题

合敬然(),郭合林(),王文清*

^{武汉理工大学数学科学研究中心武汉 430070}

收稿日期:2020-10-14 出版日期:2021-10-26 发布日期:2021-10-08
通讯作者: 王文清 E-mail:462147945@qq.com;qfguohelin@126.com
作者简介:合敬然, E-mail: 462147945@qq.com|郭合林, E-mail: qfguohelin@126.com
基金资助:
国家自然科学基金(11931012);国家自然科学基金(11871387)

A p-Laplace Eigenvalue Problem with Coercive Potentials

Jingran He(),Helin Guo(),Wenqing Wang*

^{Center of Mathematical Sciences and Department of Mathematics, Wuhan University of Technology, Wuhan 430070}

Received:2020-10-14 Online:2021-10-26 Published:2021-10-08
Contact: Wenqing Wang E-mail:462147945@qq.com;qfguohelin@126.com
Supported by:
the NSFC(11931012);the NSFC(11871387)

摘要/Abstract

摘要：

该文研究了一类带强制位势的p-Laplace特征值问题解的渐近行为.这里的位势其底部（即位势全局极小值点的集合）是一个椭球，该文证得相应参数靠近某个门槛值时，方程的解会在位势底部的椭球长轴端点处发生爆破，并给出了精确的爆破速率.

关键词: p-Laplace, 特征值问题, 渐近行为, 爆破速率

Abstract:

In this paper, we are concerned with the asymptotic behavior of solutions for a p-Laplace eigenvalue problem with coercive potentials. The bottom of the potential (The set of global minimum points of the potential) is an ellipsoid, we prove that the solutions of the problem will blow up at one of the endpoints of the major axis of the ellipsoid as the related parameter tends to a threshold value, and we also give the exact blow-up rate.

Key words: p-Laplace, Eigenvalue problem, Asymptotical behavior, Blow-up rate

中图分类号:

O175.2

合敬然,郭合林,王文清. 一类带强制位势的p-Laplace特征值问题[J]. 数学物理学报, 2021, 41(5): 1323-1332.

Jingran He,Helin Guo,Wenqing Wang. A p-Laplace Eigenvalue Problem with Coercive Potentials[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1323-1332.

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