四川大学学报（自然科学版）2024，Vol.61Issue(6)：37-41,5.DOI:10.19907/j.0490-6756.2024.061002
非线性项零点对平均曲率方程Dirichlet问题多解性的影响
Effect of the zero points of nonlinear term on the multiplicity of Dirichlet problem of mean curvature equations
摘要
Abstract
Many problems in relativity theory,such as the state of particle motion,are closely related to the mean curvature equations in Minkowski space.Meanwhile,the capillary phenomenon for compressible fluid and the characterization of corneal geometry are closely related to the mean curvature equations in Euclidean space.In this paper,we study the existence and multiplicity of positive radial solutions of the Dirichlet prob-lem of mean curvature equations in Euclidean and Minkowski spaces.Firstly,based on the special structure of the mean curvature equations,the existence of positive radial solutions is transformed into the problem of existence of fixed points of the corresponding integral operator.Secondly,the existence and multiplicity of positive radial solutions are proved by using the fixed point theorem in cones under the condition that the non-linear term of equation has zero point.The obtained results reveal the effect of the number of zero points of the nonlinear term on the number of positive radial solutions of the Dirichlet problem.关键词
平均曲率方程/正径向解/多解性Key words
Mean curvature equation/Positive radial solution/Multiplicity分类
数理科学引用本文复制引用
何志乾,苗亮英,迟昊东..非线性项零点对平均曲率方程Dirichlet问题多解性的影响[J].四川大学学报（自然科学版）,2024,61(6):37-41,5.基金项目
国家自然科学基金(12461035,12301631) （12461035,12301631）
青海省自然科学基金(2023-ZJ-949Q) （2023-ZJ-949Q）
