一阶非线性常微分方程边值问题正解的存在性  

Existence of Positive Solutions for Nonlinear First-Order Ordinary Boudary Value Problems

作　　者：武若飞 

机构地区：[1]西北师范大学,数学与统计学院,甘肃 兰州

出　　处：《理论数学》2021年第5期720-730,共11页Pure Mathematics

摘　　要：本文考察了一阶非线性常微分边值问题正解的存在性,其中f:[0,1]×[0,∞)→[0,∞),a:[0,1]→[0,∞)均为连续函数, 且∫01a(θ)dθ 】0,λ为正参数,l为常数且0 ∫01a(θ)dθ.在非线性项 f 满足超线性, 欠线性和渐近线性的条件下,本文运用不动点指数理论获得了该问题正解的存在性。In this paper, we consider the existence of positive solutions for the nonlinear first- order ordinary boundary value problems where f:[0,1]×[0,∞)→[0,∞),a:[0,1]→[0,∞) are continuous functions and ∫01a(θ)dθ >0, λ is a positive parameter, l is a constant, and 0 ∫01a(θ)dθ . Under the assumption that the nonlinear term f satisfies superlinear, sublinear and asymptotic growth conditon, the existence of positive solutions of the problem is obtained by using the fixed-point index theory.

关 键 词：正解 多解 不动点 锥 

分 类 号：O17[理学—数学]