# 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

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topPiotr 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 -

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