一维Minkowski平均曲率型方程Dirichlet问题的分歧曲线  

Bifurcation Curves of the Dirichlet Problem for the One-dimensional Minkowski-curvature Equation

作　　者：何志乾[1] 苗亮英[2] 谢笋 HE ZHIQIAN;MIAO LIANGYING;XIE SUN(School of Mathematics and Physics,Qinghai University,Xining 810016,China;School of Mathematics and Statistics,Qinghai Minzu University,Xining 810007,China)

机构地区：[1]青海大学数理学院,西宁810016 [2]青海民族大学数学与统计学院,西宁810007

出　　处：《应用数学学报》2023年第3期389-397,共9页Acta Mathematicae Applicatae Sinica

基　　金：青海省自然科学基金项目(批准号:2021-ZJ-957Q)资助项目。

摘　　要：本文运用时间映像法研究了一类非线性项不满足符号条件的Minkowski型平均曲率方程Dirichlet问题■正解的分歧曲线形状及相应正解的存在性和多解性,其中λ>0是参数,f∈C[0,∞)∩C^(2)(0,∞).本文的主要结果揭示了非线性项f的零点个数与正解个数之间的关系,推广和改进了已有文献中的相关结果.In this paper,by using the time map,we are considered with the shape of bifurcation curves as well as the existence and multiplicity of positive solutions for a class of Minkowski-curvature Dirichlet problem■in the case of the nonlinear term does not satisfy the sign condition,whereλ>0 is a parameter,f∈C[0,∞)∩C^(2)(0,∞).The results revealed the relationship between the number of the nonlinear term f and the number of the positive solutions.Our results improve and extend the existing results.

关 键 词：分歧曲线 平均曲率方程 正解 存在性 符号条件 

分 类 号：O175.8[理学—数学]