非线性一阶边值问题正解的全局结构  

Existence of positive solutions of nonlinear first order boundary value problem

作　　者：苏艳 金英姬[1] Su Yan;Jin Yingji(Department of Education,Tibet University for Nationalities,Xianyang 712082,China)

机构地区：[1]西藏民族大学教育学院,陕西咸阳712082

出　　处：《纯粹数学与应用数学》2021年第3期286-293,共8页Pure and Applied Mathematics

基　　金：国家自然科学基金(11661073);西藏自治区自然科学基金资助项目(2016 ZR-15-19).

摘　　要：微分方程的应用十分广泛,可以解决许多与导数有关的问题.物理中涉及变力的动力学问题,如空气的阻力为速度函数的落体运动等问题,很多可以用微分方程求解.运用Dancer全局分歧定理研究了一类非线性一阶微分方程边值问题正解的存在性,获得该问题正解存在的最优条件.Differential equations have a wide range of applications,and can be used to solve many problems related to derivatives.Many problems in physics involving the dynamics of variable forces,such as air resistance as a function of the velocity of the falling body motion,can be solved by differential equations.In this paper,we show the existence of positive solutions for a class of nonlinear first-order differential equation boundary value problem.By using Dancer′s global bifurcation theorem,we obtain the optimal conditions for the existence of positive solutions.

关 键 词：非线性一阶边值问题 分歧理论 正解 

分 类 号：O178[理学—数学]