Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions

Leszek Olszowy

Open Mathematics (2014)

  • Volume: 12, Issue: 4, page 623-635
  • ISSN: 2391-5455

Abstract

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This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure of noncompactness, and the linear part generates only a strongly continuous evolution system.

How to cite

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Leszek Olszowy. "Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions." Open Mathematics 12.4 (2014): 623-635. <http://eudml.org/doc/269262>.

@article{LeszekOlszowy2014,
abstract = {This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure of noncompactness, and the linear part generates only a strongly continuous evolution system.},
author = {Leszek Olszowy},
journal = {Open Mathematics},
keywords = {Fréchet space; Impulsive mild solution; Measure of noncompactness; Nonlocal condition; Semilinear differential equation; impulsive mild solution; measure of noncompactness; nonlocal condition; semilinear differential equation},
language = {eng},
number = {4},
pages = {623-635},
title = {Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions},
url = {http://eudml.org/doc/269262},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Leszek Olszowy
TI - Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions
JO - Open Mathematics
PY - 2014
VL - 12
IS - 4
SP - 623
EP - 635
AB - This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure of noncompactness, and the linear part generates only a strongly continuous evolution system.
LA - eng
KW - Fréchet space; Impulsive mild solution; Measure of noncompactness; Nonlocal condition; Semilinear differential equation; impulsive mild solution; measure of noncompactness; nonlocal condition; semilinear differential equation
UR - http://eudml.org/doc/269262
ER -

References

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