带积分边界条件的非线性二阶常微分方程多个正解的存在性
Existence of Multiple Positive Solutions for Nonlinear Second-Order Ordinary Differential Equations with Integral Boundary Conditions
DOI: 10.12677/PM.2021.116121, PDF, 下载: 324  浏览: 499  国家自然科学基金支持
作者: 康慧君：西北师范大学数学与统计学院，甘肃 兰州
关键词: 积分边界条件；二阶；多个正解；Krasnoselskii’s不动点定理；Integral Boundary Conditions； Second-Order； Multiple Positive Solutions； Krasnoselskii’s Fixed Point Theorem
摘要: 运用锥上的 Krasnoselskii’s 不动点定理,考虑了二阶积分边值问题 多个正解的存在性,其中0 < η < 1是常数,0 < λ < 2/n2是参数,f:[0,1]×[0,∞)→[0,∞)是连续函数,a:[0,1]→[0,+∞)是连续函数,且在[0,1]的任一子区间上不恒为零.
Abstract: In this paper, we study existence of multiple positive solutions for second-order ordinary differential equations with integral boundary problem by the Krasnoselskii’s fixed point theorem on cones. where 0 < η < 1 is a constant, 0 < λ < 2/n2 is a parameter, f:[0,1]×[0,∞)→[0,∞) is continuous, a:[0,1]→[0,+∞) is continuous, and a(t) ≢ 0 on any subinterval of [0,1].
文章引用：康慧君. 带积分边界条件的非线性二阶常微分方程多个正解的存在性[J]. 理论数学, 2021, 11(6): 1067-1075. https://doi.org/10.12677/PM.2021.116121

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