Differential equations with non-absolutely integrable functions in ordered Banach spaces

DOI10.1016/J.NA.2010.01.040zbMath1203.34093OpenAlexW1978095327MaRDI QIDQ965020

M. Kumpulainen, Seppo Heikkilä

Publication date: 21 April 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.2010.01.040

zbMATH Keywords

ordered Banach spacesHL integrabilityregular order coneinitial values problemsmalest and greatest solutions

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Nonlinear differential equations in abstract spaces (34G20) Denjoy and Perron integrals, other special integrals (26A39) Set functions, measures and integrals with values in ordered spaces (28B15)

Related Items (2)

On singular nonlinear distributional and impulsive initial and boundary value problems ⋮ Second order initial value problems with non-absolute integrals in ordered Banach spaces

Cites Work

• Nonsmooth and nonlocal differential equations in lattice-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
• On singular, functional, nonsmooth and implicit phi-Laplacian initial and boundary value problems
• On improper integrals and differential equations in ordered Banach spaces
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