Existence theory for integrodifferential equations and Henstock-Kurzweil integral in Banach spaces.

Sikorska-Nowak, Aneta

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

Nonlinear integrodifferential equations of mixed type in Banach spaces.

Sikorska-Nowak, Aneta, Nowak, Grzegorz (2007)

International Journal of Mathematics and Mathematical Sciences

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On the Volterra integral equation and the Henstock-Kurzweil integral.

Bugajewski, D. (1998)

Mathematica Pannonica

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Existence of solutions of second order boundary value problems with integral boundary conditions and singularities.

Ye, Guoju, Li, Xiuli (2010)

Journal of Inequalities and Applications [electronic only]

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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 $x (t) - (K) \int_{[a, t]} α (t, s) x (s) d s = f (t), t \in [a, b],$ 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 $x (t) - (K) \int_{[a, t]} α (t, s) x (s) d g (s) = f (t), t \in [a, b],$ 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.