一类二阶半正Dirichlet边值问题正解的存在性和多解性
Existence and Multiplicity of PositiveSolutions for a Class of Second-OrderDirichlet Boundary Value Problems
DOI: 10.12677/PM.2023.137206, PDF,    国家自然科学基金支持
作者: 李存丽：西北师范大学，数学与统计学院，甘肃 兰州
关键词: 正解；半正问题；不动点指数理论；上下解；Positive Solutions； Semi-Positone Problem； Fixed Point Index； Upper and Lower Solutions
摘要: 考察二阶半正 Dirichlet 边值问题 正解的存在性与多解性,其中入为正参数，f∈C([0,∞),[0,∞))，存在∧> 0，使得∈∈[0,∧]。当f 满足时，运用不动点指数理论和上下解方法证明了存在常数λ∗ > 0，使得当λ>λ∗时，问题(P) 至少存在两个正解。
Abstract: In this paper,we are considered with the existence and multiplicity of positive solutions for second-order Dirichlet boundary value problems where λ is a positive parameter, f∈C([0,∞),[0,∞)), there exists ∧> 0, such that ∈∈[0,∧]. When f satisfies , we apply a fixed point index theorem and the method of the upper and lower solutions to prove that there exists λ∗ > 0 such that the problem (P) has at least two positive solutions for λ>λ∗.
文章引用：李存丽. 一类二阶半正Dirichlet边值问题正解的存在性和多解性[J]. 理论数学, 2023, 13(7): 2007-2016. https://doi.org/10.12677/PM.2023.137206

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