A necessary and sufficient condition for the existence of positive solutions of singular boundary value problems

DOI10.1016/j.aml.2004.07.029zbMath1095.34013OpenAlexW2084348684MaRDI QIDQ812764

Yumei Xu, Lokenath Debnath, Li Shan Liu

Publication date: 24 January 2006

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2004.07.029

zbMATH Keywords

conepositive solutionssingular boundary value problemsfixed-point theorems

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Theoretical approximation of solutions to ordinary differential equations (34A45) Positive solutions to nonlinear boundary value problems for ordinary differential equations (34B18) Singular nonlinear boundary value problems for ordinary differential equations (34B16)

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Necessary and sufficient condition for the existence of positive solution to singular fractional differential equations ⋮ Multiple positive solutions of a boundary value problem for a class of \(2n\)th-order \(m\)-point singular integro-differential equations in Banach spaces ⋮ Necessary and sufficient conditions for the existence of symmetric positive solutions of singular boundary value problems ⋮ A necessary and sufficient condition for existence of positive solutions of nonlinear boundary value problems ⋮ Necessary and sufficient conditions for the existence of symmetric positive solutions of multi-point boundary value problems ⋮ Eigenvalue problem and unbounded connected branch of positive solutions to a class of singular elastic beam equations ⋮ A necessary and sufficient condition for the existence of positive solutions to a kind of singular three-point boundary value problem

Cites Work

• Existence and uniqueness theorems for fourth-order boundary value problems
• Existence and uniqueness results for the bending of an elastic beam equation at resonance
• Solvability of some fourth (and higher) order singular boundary value problems
• Positive solutions to certain classes of singular nonlinear second order boundary value problems
• Positive Solutions of Nonresonant Singular Boundary Value Problem of Second Order Differential Equations
• Fourth order two-point boundary value problems; estimates by two-sided bounds
• Fourth (and higher) order singular boundary value problems
• A nonlinear singular boundary value problem
• A Uniqueness Theorem for a Boundary Value Problem
• Multiple symmetric positive solutions for a second order boundary value problem

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