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2011 | 31 | 1 | 71-90
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Integro-differential equations on time scales with Henstock-Kurzweil delta integrals

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