Integro-differential equations on time scales with Henstock-Kurzweil delta integrals

Aneta Sikorska-Nowak

Displaying similar documents to “Integro-differential equations on time scales with Henstock-Kurzweil delta integrals”

Volterra integral equations governed by highly oscillatory functions on the time scale.

Satco, Bianca (2009)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion

Tuo-Yeong Lee (2005)

Mathematica Bohemica

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It is shown that a Banach-valued Henstock-Kurzweil integrable function on an $m$ -dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function $f {[0, 1]}^{2} ⟶ ℝ$ and a continuous function $F {[0, 1]}^{2} ⟶ ℝ$ such that $(¶) \int_{0}^{x} \{(¶) \int_{0}^{y} f (u, v) d v\} d u = (¶) \int_{0}^{y} \{(¶) \int_{0}^{x} f (u, v) d u\} d v = F (x, y)$ for all $(x, y) \in {[0, 1]}^{2}$ .

A full characterization of multipliers for the strong $ρ$ -integral in the euclidean space

Lee Tuo-Yeong (2004)

Czechoslovak Mathematical Journal

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We study a generalization of the classical Henstock-Kurzweil integral, known as the strong $ρ$ -integral, introduced by Jarník and Kurzweil. Let $(𝒮_{ρ} (E), ∥ \cdot ∥)$ be the space of all strongly $ρ$ -integrable functions on a multidimensional compact interval $E$ , equipped with the Alexiewicz norm $∥ \cdot ∥$ . We show that each element in the dual space of $(𝒮_{ρ} (E), ∥ \cdot ∥)$ can be represented as a strong $ρ$ -integral. Consequently, we prove that $f g$ is strongly $ρ$ -integrable on $E$ for each strongly $ρ$ -integrable function $f$ if and only if $g$ is...

The $L^{r}$ Henstock-Kurzweil integral

Paul M. Musial, Yoram Sagher (2004)

Studia Mathematica

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We present a method of integration along the lines of the Henstock-Kurzweil integral. All $L^{r}$ -derivatives are integrable in this method.

Differential equations in banach space and henstock-kurzweil integrals

Ireneusz Kubiaczyk, Aneta Sikorska (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, using the properties of the Henstock-Kurzweil integral and corresponding theorems, we prove the existence theorem for the equation x' = f(t,x) and inclusion x' ∈ F(t,x) in a Banach space, where f is Henstock-Kurzweil integrable and satisfies some conditions.

On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock-Kurzweil integrals

Aneta Sikorska-Nowak (2004)

Annales Polonici Mathematici

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We prove some existence theorems for nonlinear integral equations of the Urysohn type $x (t) = φ (t) + λ \int_{0}^{a} f (t, s, x (s)) d s$ and Volterra type $x (t) = φ (t) + \int_{0}^{t} f (t, s, x (s)) d s$ , $t \in I_{a} = [0, a]$ , where f and φ are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.

Volterra integral inclusions via Henstock-Kurzweil-Pettis integral

Bianca Satco (2006)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, we prove the existence of continuous solutions of a Volterra integral inclusion involving the Henstock-Kurzweil-Pettis integral. Since this kind of integral is more general than the Bochner, Pettis and Henstock integrals, our result extends many of the results previously obtained in the single-valued setting or in the set-valued case.

Some characterizations of the primitive of strong Henstock-Kurzweil integrable functions

Guoju Ye (2006)

Mathematica Bohemica

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In this paper we give some complete characterizations of the primitive of strongly Henstock-Kurzweil integrable functions which are defined on $ℝ^{m}$ with values in a Banach space.