On the semilinear integro-differential nonlocal Cauchy problem

Piotr Majcher; Magdalena Roszak

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2005)

  • Volume: 25, Issue: 1, page 5-18
  • ISSN: 1509-9407

Abstract

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In this paper, we prove an existence theorem for the pseudo-non-local Cauchy problem x ' ( t ) + A x ( t ) = f ( t , x ( t ) , ∫ t ₀ t k ( t , s , x ( s ) ) d s ) , 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.

How to cite

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Piotr Majcher, and Magdalena Roszak. "On the semilinear integro-differential nonlocal Cauchy problem." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 25.1 (2005): 5-18. <http://eudml.org/doc/271539>.

@article{PiotrMajcher2005,
abstract = {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.},
author = {Piotr Majcher, Magdalena Roszak},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {integro-differential equations; measure of weak non-compactness; non-local problem; pseudo-nonlocal Cauchy problem; semigroup; Banach space},
language = {eng},
number = {1},
pages = {5-18},
title = {On the semilinear integro-differential nonlocal Cauchy problem},
url = {http://eudml.org/doc/271539},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Piotr Majcher
AU - Magdalena Roszak
TI - On the semilinear integro-differential nonlocal Cauchy problem
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2005
VL - 25
IS - 1
SP - 5
EP - 18
AB - 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.
LA - eng
KW - integro-differential equations; measure of weak non-compactness; non-local problem; pseudo-nonlocal Cauchy problem; semigroup; Banach space
UR - http://eudml.org/doc/271539
ER -

References

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