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

Aneta Sikorska-Nowak

Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 31 (2011), p. 71-90 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2011-01-01

Zbl 1257.34076

EUDML-ID : urn:eudml:doc:271148

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