On the semilinear integro-differential nonlocal Cauchy problem

• Autorzy: Piotr Majcher , Magdalena Roszak
• Języki publikacji: EN

Abstrakty

EN

In this paper, we prove an existence theorem for the pseudo-non-local Cauchy problem $x'(t) + Ax(t) = f(t,x(t),∫_{t₀}^{t} k(t,s,x(s))ds)$, 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.

Słowa kluczowe

EN

integro-differential equations; measure of weak non-compactness; non-local problem

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 45J05: Integro-ordinary differential equations
• 34G20: Nonlinear equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2005
• Tom: 25
• Numer: 1
• Strony: 5-18

Daty

wydano

2005

otrzymano

2004-01-01

Twórcy

autor

Piotr Majcher

• Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

autor

Magdalena Roszak

• Institute of Mathematics and Physics, University of Technology and Agriculture, Al. Prof. S. Kaliskiego 7, 85-796 Bydgoszcz

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1055