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

• Autorzy: Aneta Sikorska-Nowak
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove existence theorems for integro - differential equations
$x^Δ (t) = f(t,x(t),∫₀^t k(t,s,x(s))Δs)$,
t ∈ Iₐ = [0,a] ∩ T, a ∈ R₊,
x(0) = x₀
where T denotes a time scale (nonempty closed subset of real numbers R), Iₐ is a time scale interval. Functions f,k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil delta integral, which generalizes the Henstock-Kurzweil integral.
Additionally, functions f and k satisfy some boundary conditions and conditions expressed in terms of measures of noncompactness. Moreover, we prove an Ambrosetti type lemma on a time scale.

Słowa kluczowe

EN

integro-differential equations; nonlinear Volterra integral equation; time scales; Henstock-Kurzweil delta integral; HL delta integral; Banach space; fixed point; measure of noncompactness; Carathéodory solutions

Kategorie tematyczne

• 34D09: Dichotomy, trichotomy
• 34D99: None of the above, but in this section

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2011
• Tom: 31
• Numer: 1
• Strony: 71-90

Daty

wydano

2011

otrzymano

2010-04-20

Twórcy

autor

Aneta Sikorska-Nowak

• Adam Mickiewicz University, Faculty of Mathematics and Computer Science, Poznań, Poland

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Identyfikatory

DOI

10.7151/dmdico.1128