On the semilinear integro-differential nonlocal Cauchy problem

Piotr Majcher ; Magdalena Roszak

Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 25 (2005), p. 5-18 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper, we prove an existence theorem for the pseudo-non-local Cauchy problem $x^{\prime }(t) + Ax(t) = f(t,x(t),∫_{t₀}^{t} k(t,s,x(s))ds)$, x₀(t₀) = x₀ - g(x), where A is the infinitesimal generator of a C₀ semigroup of operator ${T(t)}_{t > 0}$ on a Banach space. The functions f,g are weakly-weakly sequentially continuous and the integral is taken in the sense of Pettis.

Détail

Publié le : 2005-01-01

Zbl 1111.45010

EUDML-ID : urn:eudml:doc:271539

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