Global existence for functional semilinear integro-differential equations

Sotiris K. Ntouyas

Archivum Mathematicum (1998)

  • Volume: 034, Issue: 2, page 239-256
  • ISSN: 0044-8753

Abstract

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In this paper, we study the global existence of solutions for first and second order initial value problems for functional semilinear integrodifferential equations in Banach space, by using the Leray-Schauder Alternative or the Nonlinear Alternative for contractive maps.

How to cite

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Ntouyas, Sotiris K.. "Global existence for functional semilinear integro-differential equations." Archivum Mathematicum 034.2 (1998): 239-256. <http://eudml.org/doc/248203>.

@article{Ntouyas1998,
abstract = {In this paper, we study the global existence of solutions for first and second order initial value problems for functional semilinear integrodifferential equations in Banach space, by using the Leray-Schauder Alternative or the Nonlinear Alternative for contractive maps.},
author = {Ntouyas, Sotiris K.},
journal = {Archivum Mathematicum},
keywords = {Leray-Schauder Alternative; a priori bounds; partial functional integrodifferential equations; global existence; Leray-Schauder alternative; a priori bounds},
language = {eng},
number = {2},
pages = {239-256},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Global existence for functional semilinear integro-differential equations},
url = {http://eudml.org/doc/248203},
volume = {034},
year = {1998},
}

TY - JOUR
AU - Ntouyas, Sotiris K.
TI - Global existence for functional semilinear integro-differential equations
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 2
SP - 239
EP - 256
AB - In this paper, we study the global existence of solutions for first and second order initial value problems for functional semilinear integrodifferential equations in Banach space, by using the Leray-Schauder Alternative or the Nonlinear Alternative for contractive maps.
LA - eng
KW - Leray-Schauder Alternative; a priori bounds; partial functional integrodifferential equations; global existence; Leray-Schauder alternative; a priori bounds
UR - http://eudml.org/doc/248203
ER -

References

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  1. Second order semilinear Volterra integrodifferential equation in Banach space,, Ann. Pol. Math. 57 (1992), 231–241. (1992) Zbl0786.45013MR1201850
  2. Fixed Point Theory, Vol. I, Monographie Matematyczne, PNW Warsawa, 1982. (1982) 
  3. Partial differential equations, Holt, Rinehat and Winston,, New York, 1969. (1969) Zbl0224.35002MR0445088
  4. Resultats du type de Leray-Schauder pour des contractions multivoques, Topol. Methods Nonlinear Anal. 4 (1994), 197–208. (1994) MR1321812
  5. Topological transversality. Applications to initial value problems, Ann. Pol. Math. 48 (1988), 247–252. (1988) MR0978675
  6. Existence results for differential delay equations-I, J. Differential Equations 102 (1993), 342–359. (1993) MR1216733
  7. An integro-differential equation with applications in heat flow, Quart. Appl. Math. 35 (1977/78), 1–19. (1977/78) MR0452184
  8. Existence results for initial value problems for neutral functional differential equations, J. Differential Equations 114 (1994), 527–537. (1994) MR1303038
  9. Initial and boundary value problems for functional integrodifferential equations, J. Appl. Math. Stoch. Analysis 10 (1997), 157–168. (1997) MR1453468
  10. Global existence for functional integrodifferential equations of delay and neutral type, Applicable Analysis 54 (1994), 251–262. (1994) MR1379636
  11. Cosine families and abstract nonlinear second order differential equations, Acta Math. Hungarica 32 (1978), 75–96. (1978) MR0499581
  12. An abstract second order semilinear Volterra integrodifferential equation, SIAM J. Math. Anal. 10 (1979), 412–424. (1979) MR0523855
  13. Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc. 200 (1974), 395–418. (1974) MR0382808
  14. An abstract semilinear Volterra integrodifferential equation, Proc. Amer. Math. Soc. 69 (1978), 255–260. (1978) Zbl0388.45012MR0467214
  15. A continuous differential equation in Hilbert space without existence, Funkcial. Ekvac. 13 (1970), 19–21. (1970) Zbl0248.34061MR0264196

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