Impulsive retarded differential equations in Banach spaces via Bochner-Lebesgue and Henstock integrals

DOI10.1016/S0362-546X(01)00769-6zbMath1011.34070OpenAlexW2009617258MaRDI QIDQ1612581

Plácido Zoega Táboas, Marcia Federson

Publication date: 25 August 2002

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/s0362-546x(01)00769-6

zbMATH Keywords

existence theoremsimpulsesHenstock integralsretarded equations

Mathematics Subject Classification ID

Functional-differential equations with impulses (34K45) Functional-differential equations in abstract spaces (34K30)

Related Items (14)

Semilinear evolution equations with distributed measures ⋮ Existence results for Urysohn integral inclusions involving the Henstock integral ⋮ A Cauchy Problem on Time Scales with Applications ⋮ On singular nonlinear distributional and impulsive initial and boundary value problems ⋮ Second order initial value problems with non-absolute integrals in ordered Banach spaces ⋮ Regulated solutions for nonlinear measure driven equations ⋮ Equations containing locally Henstock-Kurzweil integrable functions. ⋮ Impulsive nonlocal differential equations through differential equations on time scales ⋮ Solution tube method for impulsive periodic differential inclusions of first order ⋮ A Komlós-type theorem for the set-valued Henstock-Kurzweil-Pettis integral and applications ⋮ The set of solutions of Volterra and Urysohn integral equations in Banach spaces ⋮ On the existence of weak solutions of nonlinear integral equations in Banach spaces ⋮ Convergence theorems for HL integrable vector-valued functions with applications ⋮ A new result on impulsive differential equations involving non-absolutely convergent integrals

Cites Work

• The Perron integral in ordinary differential equations
• On \(x'=f(t,x)\) and Henstock-Kurzweil integrals
• On the solution of \((dy/dx)_{ap}=f(x,y)\)
• Theory of functional differential equations. 2nd ed
• Topological dynamics of ordinary differential equations and Kurzweil equations
• On necessary conditions for Henstock integrability
• Linear integral equations of Volterra concerning Henstock integrals
• The fundamental theorem of calculus for multidimensional Banach space-valued Henstock vector integrals
• On retarded functional differential equations and Henstock-Kurzweil integrals
• Volterra-Stieltjes integral equations with linear constraints and discontinuous solutions
• A Unified Theory of Integration
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