Uniqueness and multiplicity of positive solutions for one-dimensional prescribed mean curvature equation in Minkowski space

被引：9

作者：

He, Zhiqian ^{[1
]}

Miao, Liangying ^{[2
]}

机构：

[1] Qinghai Univ, Dept Basic Teaching & Res, Xining 810016, Peoples R China

[2] Qinghai Nationalities Univ, Sch Math & Stat, Xining 810007, Peoples R China

来源：

AIMS MATHEMATICS | 2020年 / 5卷 / 04期

关键词：

mean curvature equation; positive solutions; multiplicity; uniqueness; cone; DIRICHLET PROBLEM; RADIAL SOLUTIONS; HYPERSURFACES;

D O I：

10.3934/math.2020249

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the uniqueness and multiplicity of positive solutions of one-dimensional prescribed mean curvature equation {-(u'/root 1 - u'(2))' = lambda f(u), u(x) > 0, -1 < x < 1, u(-1) = u(1) = 0, where lambda is a positive parameter. The main tool is the fixed point index in cones.

引用

页码：3840 / 3850

页数：11

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