Displaying similar documents to “Existence theory for integrodifferential equations and Henstock-Kurzweil integral in Banach spaces.”

Linear Volterra-Stieltjes integral equations in the sense of the Kurzweil-Henstock integral

Márcia Federson, Ricardo Bianconi (2001)

Archivum Mathematicum

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In 1990, Hönig proved that the linear Volterra integral equation x t - ( K ) ∫ a , t α t , s x s d s = f t , t ∈ a , b , where the functions are Banach space-valued and f is a Kurzweil integrable function defined on a compact interval a , b of the real line ℝ , admits one and only one solution in the space of the Kurzweil integrable functions with resolvent given by the Neumann series. In the present paper, we extend Hönig’s result to the linear Volterra-Stieltjes integral equation x t - ( K ) ∫ a , t α t , s x s d g s = f t , t ∈ a , b , in a real-valued context.

Some fixed point theorems and existence of weak solutions of Volterra integral equation under Henstock-Kurzweil-Pettis integrability

Afif Ben Amar (2011)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we examine the set of weakly continuous solutions for a Volterra integral equation in Henstock-Kurzweil-Pettis integrability settings. Our result extends those obtained in several kinds of integrability settings. Besides, we prove some new fixed point theorems for function spaces relative to the weak topology which are basic in our considerations and comprise the theory of differential and integral equations in Banach spaces.

Equations containing locally Henstock-Kurzweil integrable functions

Seppo Heikkilä, Guoju Ye (2012)

Applications of Mathematics

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A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions.

The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem

Mieczysław Cichoń, Ireneusz Kubiaczyk, Sikorska-Nowak, Aneta Sikorska-Nowak, Aneta (2004)

Czechoslovak Mathematical Journal

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In this paper we prove an existence theorem for the Cauchy problem x ' ( t ) = f ( t , x ( t ) ) , x ( 0 ) = x 0 , t ∈ I α = [ 0 , α ] using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of measures of weak noncompactness.