Existence of mild solutions of second order initial value problems for delay integrodifferential inclusions with nonlocal conditions

Mouffak Benchohra; Sotiris K. Ntouyas

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 4, page 613-622
  • ISSN: 0862-7959

Abstract

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In this paper we investigate the existence of mild solutions to second order initial value problems for a class of delay integrodifferential inclusions with nonlocal conditions. We rely on a fixed point theorem for condensing maps due to Martelli.

How to cite

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Benchohra, Mouffak, and Ntouyas, Sotiris K.. "Existence of mild solutions of second order initial value problems for delay integrodifferential inclusions with nonlocal conditions." Mathematica Bohemica 127.4 (2002): 613-622. <http://eudml.org/doc/249028>.

@article{Benchohra2002,
abstract = {In this paper we investigate the existence of mild solutions to second order initial value problems for a class of delay integrodifferential inclusions with nonlocal conditions. We rely on a fixed point theorem for condensing maps due to Martelli.},
author = {Benchohra, Mouffak, Ntouyas, Sotiris K.},
journal = {Mathematica Bohemica},
keywords = {initial value problems; convex multivalued map; mild solution; evolution inclusion; nonlocal condition; fixed point; initial value problems; convex multivalued map; mild solution; evolution inclusion; nonlocal condition; fixed point},
language = {eng},
number = {4},
pages = {613-622},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of mild solutions of second order initial value problems for delay integrodifferential inclusions with nonlocal conditions},
url = {http://eudml.org/doc/249028},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Benchohra, Mouffak
AU - Ntouyas, Sotiris K.
TI - Existence of mild solutions of second order initial value problems for delay integrodifferential inclusions with nonlocal conditions
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 4
SP - 613
EP - 622
AB - In this paper we investigate the existence of mild solutions to second order initial value problems for a class of delay integrodifferential inclusions with nonlocal conditions. We rely on a fixed point theorem for condensing maps due to Martelli.
LA - eng
KW - initial value problems; convex multivalued map; mild solution; evolution inclusion; nonlocal condition; fixed point; initial value problems; convex multivalued map; mild solution; evolution inclusion; nonlocal condition; fixed point
UR - http://eudml.org/doc/249028
ER -

References

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  1. Existence of solutions of a delay differential equation with nonlocal condition, Indian J. Pure Appl. Math. 27 (1996), 443–449. (1996) MR1387239
  2. Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, 1980. (1980) MR0591679
  3. Existence of mild solutions for certain delay semilinear evolution inclusions with nonlocal conditions, Dynam. Systems Appl. 9 (2000), 405–412. (2000) MR1844640
  4. Existence and uniqueness of solutions of semilinear evolution nonlocal Cauchy problem, Zeszyty Nauk. Politech. Rzeszowskiej Mat. Fiz. (1993), 109–112. (1993) MR1274697
  5. 10.1016/0022-247X(91)90164-U, J. Math. Anal. Appl. 162 (1991), 494–505. (1991) Zbl0748.34040MR1137634DOI10.1016/0022-247X(91)90164-U
  6. Multivalued Differential Equations, Walter de Gruyter, Berlin, 1992. (1992) Zbl0820.34009MR1189795
  7. Ordinary differential equations in linear topological spaces, I, J. Differ. Equations 5 (1968), 72–105. (1968) MR0277860
  8. 10.1016/0022-0396(69)90117-X, J. Differ. Equations 6 (1969), 50–70. (1969) MR0277861DOI10.1016/0022-0396(69)90117-X
  9. Semigroups of Linear Operators and Applications, Oxford Univ. Press, New York, 1985. (1985) Zbl0592.47034MR0790497
  10. Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker, New York, 1994. (1994) MR1280028
  11. Handbook of Multivalued Analysis, Volume I: Theory, Kluwer, Dordrecht, 1997. (1997) MR1485775
  12. An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781–786. (1965) MR0196178
  13. A Rothe’s type theorem for non-compact acyclic-valued map, Boll. Un. Mat. Ital. 4 (1975), 70–76. (1975) MR0394752
  14. 10.1006/jmaa.1997.5425, J. Math. Anal. Appl. 210 (1997), 679–687. (1997) MR1453198DOI10.1006/jmaa.1997.5425
  15. 10.1080/00036819708840609, Appl. Anal. 67 (1997), 245–257. (1997) MR1614061DOI10.1080/00036819708840609
  16. Global existence results for certain second order delay integrodifferential equations with nonlocal conditions, Dynam. Systems. Appl. 7 (1998), 415–426. (1998) Zbl0914.35148MR1639604
  17. Second order differential equations in Banach spaces, Proc. Int. Symp. on Nonlinear Equations in Abstract Spaces, Academic Press, New York, 1978, pp. 331–361. (1978) MR0502551
  18. 10.1007/BF01902205, Acta Math. Hung. 32 (1978), 75–96. (1978) MR0499581DOI10.1007/BF01902205
  19. Functional Analysis, 6th edn, Springer, Berlin, 1980. (1980) MR0617913

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