| Minkowski空间一维给定平均曲率型方程Robin问题正解的存在性和多解性 |
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| 引用本文： | 苗亮英,何志乾. Minkowski空间一维给定平均曲率型方程Robin问题正解的存在性和多解性[J]. 吉林大学学报(理学版), 2021, 59(3): 559-562. DOI: 10.13413/j.cnki.jdxblxb.2020222 |
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| 作者姓名： | 苗亮英 何志乾 |
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| 作者单位： | 1. 青海民族大学 数学与统计学院, 西宁 810007; 2. 青海大学 基础课教学研究部, 西宁 810016 |
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| 摘 要： | 基于锥上的不动点指数理论,通过构造适当的锥,讨论Minkowski空间中一维给定平均曲率方程Robin问题-(u'/√1-u')'=λa(t)f(u),t∈(0,1),u'(0)=u(1)=0正解的存在性和多解性,得到了非线性项f的零点个数与该Robin问题正解个数的关系.其中:λ是正参数;a∈C[0,1];f∈C([...
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| 关 键 词： | 平均曲率问题 不动点指数 正解 正解的个数 |
| 收稿时间： | 2020-07-29 |
Existence and Multiplicity of Positive Solutions for Robin Problem of One-Dimensional Prescribed Mean Curvature Equation in Minkowski Space |
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| MIAO Liangying,HE Zhiqian. Existence and Multiplicity of Positive Solutions for Robin Problem of One-Dimensional Prescribed Mean Curvature Equation in Minkowski Space[J]. Journal of Jilin University: Sci Ed, 2021, 59(3): 559-562. DOI: 10.13413/j.cnki.jdxblxb.2020222 |
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| Authors: | MIAO Liangying HE Zhiqian |
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| Affiliation: | 1. School of Mathematics and Statistics, Qinghai Nationalities University, Xining 810007, China;
2. Teaching and Research Department of Basic Courses, Qinghai University, Xining 810016, China |
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| Abstract: | Based on the fixed point index theorem of cone, by constructing a proper cone, we discuss the existence and multiplicity of positive solutions for Robin problem of one-dimensional prescribed mean curvature equation in Minkowski space and obtain relationship between the number of the zeros of the nonlinear term f and the number of positive solutions of the Robin problems, where λ is a positive parameter, a∈C［0,1］, f∈C(［0,∞),［0,∞)) and there exist two sequences of positive numbers ai and bi with f(ai)=0, f(bi)=0 and f(s)>0 in s∈(ai,bi), and aii≤ai+1i+1 for i=1,2,…,n. |
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| Keywords: | mean curvature problem fixed point index positive solution number of positive solution |
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