一类半正二阶Neumann边值问题正解的存在性

doi:10.6040/j.issn.1671-9352.0.2022.222

摘要/Abstract

摘要： 考察一类半正二阶Neumann边值问题{u″(t)+a(t)u(t)=λf(t,u(t)), 0π²)/4, f∈C(［0,1］×R⁺,R)且f(t,0)<0。证得存在一个正数λ₀,使得当0<λ<λ₀时,该问题存在一个正解。主要结果的证明基于拓扑度理论。

关键词: Neumann边值问题, 正解, 半正, 拓扑度

Abstract: This paper considers the existence of positive solutions of second order Neumann boundary value problems{u″(t)+a(t)u(t)=λf(t,u(t)), 0where λ is a positive parameter, a∈C［0,1］ and 0π²)/4, f∈C(［0,1］×R⁺,R)and f(t,0)<0. The proof of that there exists a positive constant λ₀ such that the problem has one positive solution for 0<λ<λ₀. The proof of the main results is based on topological degree theory.

Key words: Neumann boundary value problem, positive solution, semipositone, topological degree

中图分类号:

O175.8

雷想兵. 一类半正二阶Neumann边值问题正解的存在性[J]. 《山东大学学报(理学版)》, 2023, 58(4): 82-88.

LEI Xiang-bing. Existence of positive solutions for a class of semipositone second order Neumann boundary value problems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(4): 82-88.

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