Equations containing locally Henstock-Kurzweil integrable functions.

DOI10.1007/s10492-012-0034-7zbMath1274.45017OpenAlexW2047996035MaRDI QIDQ1941780

Guoju Ye, Seppo Heikkilä

Publication date: 21 March 2013

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10338.dmlcz/143003

zbMATH Keywords

fixed pointCauchy problemVolterra integral equationHenstock-Kurzweil integralordered Banach spacefunctional integral equation

Mathematics Subject Classification ID

Ordinary differential equations with impulses (34A37) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07) Denjoy and Perron integrals, other special integrals (26A39) Abstract integral equations, integral equations in abstract spaces (45N05) Ordered normed spaces (46B40) Set functions, measures and integrals with values in ordered spaces (28B15)

Cites Work

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• Generalized ODE approach to impulsive retarded functional differential equations
• Convergence and comparison results for Henstock-Kurzweil and McShane integrable vector-valued functions
• Nonlinear integrodifferential equations of mixed type in Banach spaces
• On discontinuous implicit and explicit abstract impulsive boundary value problems
• Impulsive retarded differential equations in Banach spaces via Bochner-Lebesgue and Henstock integrals
• On singularity of Henstock integrable functions
• Existence theory for integrodifferential equations and Henstock-Kurzweil integral in Banach spaces
• On improper integrals and differential equations in ordered Banach spaces
• Linear Fredholm Integral Equations and the Integral of Kurzweil
• On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock–Kurzweil integrals

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