Existence of mild solutions on semiinfinite interval for first order differential equation with nonlocal condition

Mouffak Benchohra; Sotiris K. Ntouyas

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 3, page 485-491
  • ISSN: 0010-2628

Abstract

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In this paper we investigate the existence of mild solutions defined on a semiinfinite interval for initial value problems for a differential equation with a nonlocal condition. The results is based on the Schauder-Tychonoff fixed point theorem and rely on a priori bounds on solutions.

How to cite

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Benchohra, Mouffak, and Ntouyas, Sotiris K.. "Existence of mild solutions on semiinfinite interval for first order differential equation with nonlocal condition." Commentationes Mathematicae Universitatis Carolinae 41.3 (2000): 485-491. <http://eudml.org/doc/248616>.

@article{Benchohra2000,
abstract = {In this paper we investigate the existence of mild solutions defined on a semiinfinite interval for initial value problems for a differential equation with a nonlocal condition. The results is based on the Schauder-Tychonoff fixed point theorem and rely on a priori bounds on solutions.},
author = {Benchohra, Mouffak, Ntouyas, Sotiris K.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {initial value problems; mild solution; semiinfinite interval; nonlocal condition; fixed point; initial value problems; mild solution; semiinfinite interval; nonlocal condition; fixed-point},
language = {eng},
number = {3},
pages = {485-491},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Existence of mild solutions on semiinfinite interval for first order differential equation with nonlocal condition},
url = {http://eudml.org/doc/248616},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Benchohra, Mouffak
AU - Ntouyas, Sotiris K.
TI - Existence of mild solutions on semiinfinite interval for first order differential equation with nonlocal condition
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 3
SP - 485
EP - 491
AB - In this paper we investigate the existence of mild solutions defined on a semiinfinite interval for initial value problems for a differential equation with a nonlocal condition. The results is based on the Schauder-Tychonoff fixed point theorem and rely on a priori bounds on solutions.
LA - eng
KW - initial value problems; mild solution; semiinfinite interval; nonlocal condition; fixed point; initial value problems; mild solution; semiinfinite interval; nonlocal condition; fixed-point
UR - http://eudml.org/doc/248616
ER -

References

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  8. Dauer J.P., Balachandran K., Existence of solutions for an integrodifferential equation with nonlocal condition in Banach spaces, Libertas Math. 16 (1996), 133-143. (1996) Zbl0862.45016MR1412536
  9. Dugundji J., Granas A., Fixed Point Theory, Monografie Mat., PWN, Warsaw, 1982. Zbl1025.47002MR0660439
  10. Goldstein J.A., Semigroups of Linear Operators and Applications, Oxford New York (1985). (1985) Zbl0592.47034MR0790497
  11. Ntouyas S.K., Tsamatos P.Ch., Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl. 210 (1997), 679-687. (1997) Zbl0884.34069MR1453198
  12. Ntouyas S.K., Tsamatos P.Ch., Global existence for semilinear evolution integrodifferential equations with delay and nonlocal conditions, Appl. Anal. 64 (1997), 99-105. (1997) Zbl0874.35126MR1460074
  13. Yosida K., Functional Analysis, Springer-Verlag Berlin (1980). (1980) Zbl0435.46002MR0617913

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