Second order initial value problems with non-absolute integrals in ordered Banach spaces

DOI10.1016/J.NA.2010.09.040zbMath1221.34160OpenAlexW2039983555MaRDI QIDQ611197

M. Kumpulainen, Seppo Heikkilä

Publication date: 14 December 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.09.040

zbMATH Keywords

initial value problemsingular problemordered Banach spacenonlocal problemdiscontinuous problemfunctional problemgreatest solutionHL integrabilityimplicit problemregular order conesmallest solution

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Nonlinear differential equations in abstract spaces (34G20) Fixed-point theorems (47H10) Linear operators on function spaces (general) (47B38) Discontinuous ordinary differential equations (34A36) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07) Denjoy and Perron integrals, other special integrals (26A39) Set functions, measures and integrals with values in ordered spaces (28B15)

Cites Work

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• Nonsmooth and nonlocal differential equations in lattice-ordered Banach spaces
• Differential equations with non-absolutely integrable functions in ordered Banach spaces
• Convergence theorems for HL integrable vector-valued functions with applications
• Nonlinear Urysohn discrete equations on the infinite interval: a fixed-point approach
• Impulsive retarded differential equations in Banach spaces via Bochner-Lebesgue and Henstock integrals
• On singularity of Henstock integrable functions
• On singular, functional, nonsmooth and implicit phi-Laplacian initial and boundary value problems
• On improper integrals and differential equations in ordered Banach spaces
• Fixed Point Theory in Ordered Sets and Applications

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