Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2016, Cilt: 4 Sayı: 2, 174 - 179, 01.03.2016

Öz

Kaynakça

  • J. P. Aubin, A. Cellina; Differential inclusions, Springer-Verlag, 1984.
  • C. Berge; Espaces topologiques, fonctions set-valueds, Dunod, Paris, 1966.
  • L. Boudjenah; Existence of the solutions of the paratingent equation with delayed argument. Electron. J. Diff. Eqns., Vol. 2005, No.14, 1-8, 2005.
  • L Boudjenah; On the properties of the set solutions of a class of paratingent equation with delay. British Journal of Mathematics & Computer Science 4 (14): 1999-2003, 2014.
  • E. Campu; Equations diff´erentielles au paratingent `a retardement, dans les espaces de Banach. Th´eoreme d’existence des solutions. Rev. Roum. Math. Pures Appl. 20, 631-657 ,1975.
  • E, Campu ; Approximation des solutions des ´equations diff´erentielles au paratingent `a retardement, dans les espaces de Banach. Rev. Roum. Math. Pures Appl. 25, 509-518,1980.
  • C. Castaing, A. G. Ibrahim; Functional differential inclusions on closed sets in Banach spaces. Adv. Math. Eco. 2, 21-39, 2000.
  • K. Deimling; Multivalued differential equations, De Gruyter Ser. Nonlinear Anal. Appl. 1, Walter de Gruyter, Berlin, New York, 1992.
  • H.Frankowska, F.Rampazzo ; Filippov’s and Filippov-Wasewski theorems on closed domains. J. Diff. Equ, 161, 449-478, 2000.
  • G. Haddad; Monotone trajectories of differential inclusions and functional differential inclusions with memory, Israel J. Math. 39(1-2), 83-100. 1982.
  • G. Haddad; Monotone viable trajectories for functional differential inclusions with memory. J. Diff. Eq. 42, 1-24, 1981.
  • G. Haddad; Functional viability theorems for functional differential inclusions with memory. Ann. Inst. Henri Poincar´e I (3), 179-204, 1984.
  • G. Haddad, J. M. Lasry; Periodic solutions of functional differential inclusions and fixed points of -selectionable correspondences. J. Math. Anal. Appl. 96, 295-312, 1993.
  • M. Hukuhara; Sur l’application semi-continue dont la valeur est un compact convexe. RIMS-11, Res. Inst. Math. Sci. Kyoto. Univ. 941-945, 1963.
  • M. Kamenskii, V.Obukhovskii, P. Zecca; Condensing multivalued maps and semilinear differential inclusions in Banach spaces, De Gruyter Ser. Nonlinear Anal. Appl. 7, Walter de Gruyter, Berlin, New York, 2001.
  • M. Kisielewicz; Differential Inclusions and Optimal Control. Kluwer, Dordrecht, The Netherlands, 1991.
  • B. Kryzowa; Equation au paratingenta argument retard´e. Ann. Univ. Marie Curie-Sklodwska. Sectio A, 17, 7-18, 1965. B. Kryzowa; Sur les familles de solutions des ´equation au paratingenta argument retarde. Ann. Univ. Marie Curie-Sklodwska. Sectio A, 17, 19-24, 1965.
  • A. D. Myshkis; General theory of differential equations with delayed argument, Uspehi Matem. Nauk 4, no. 5, 1949, 99-141 (in Russian)
  • S. Raczynski; Differential inclusions in system simulation. Trans. Society for Computer Simulation, Vol. 13. No. 1, 47-54. 1996.
  • S. Raczynski; A market model: uncertainty and reachable sets. Int. J. Simul. Multisci. Des. Optim. 6, A2, 2015.
  • S. Raczynski; Creating galaxies on a PC. Simulation, Vol 74, No. 3, 161-166, 2000.
  • G. V. Smirnov; Introduction to the theory of differential inclusions, Amer. Math. Soc., Providence, R.I. 2002.
  • E.D Sontag; An infinite-time relaxation theorem for differential inclusions. in Proc. Amer.Math. Soc., V 131, N◦ 2, 487-499, 2001.
  • E.D Sontag ; A relaxation theorem for differential inclusions with applications to stability properties. in Mathematical Theory of Networks and Systems (D. Gilliam and J. Rosenthal, eds.), 12 pages, August 2002, Electronic Proceedings of MTNS-2002.
  • A. Syam; Contribution a letude des inclusion differentielles. Doctorat Thesis, Universite Montpellier II, 1993.
  • A. Turowicz; Sur les trajectoires et les quasitrajectoires des systemes de commande nonlineaires. Bull. Acad. Polon. Ser. Sci. Math., Astr., Phys, Vol 10, 529-531, 1963.
  • T. Wasewski; Sur une generalisation de la notion des solutions dune equation au contingent. Bull. Acad. Pol. Sci. Ser. Math. Astronom. Physi. 10 No. 1. Warszawa, 1962.
  • T. Wasewski; Sur les syst`emes de commande non lineaires dont le contredomaine n’est pas forcement convexe. Bull. Acad. Pol. Sci. Ser. Math. Astronom. Physi. 10 No. 1. Warswa. 1962.
  • T.Wazewski; Sur un systeme de commande dont les trajectoires coincident avec les quasitrajectoires d’un syst`eme de commande donn´e. Bull. Acad. Pol. Sci. Ser. Math., Astronom., Physi. 11, N◦ 3. Warszawa 1963.
  • W. Zygmunt; On a certain pratingent equation with a deviated argument. Ann. Univ. Marie. Curie-Sklodwska. Lublin. Polonia. 18, 14, 127-135, 1974.
  • W. Zygmunt; On some properties of a certain family of solutions of the paratingent equation. Ann. Univ.Marie Curie-Sklodowska, Lublin. Polonia. Sect. A -28, 136-141,1976.

On the structure of the set solutions of a class of paratingent equation with delayed argument

Yıl 2016, Cilt: 4 Sayı: 2, 174 - 179, 01.03.2016

Öz



In this paper we
will study the main properties of the set solutions of the paratingent equation
(type differential inclusion) with delayed argument of the form: (Ptx)(t)

F([x]t ) for t ≥ 0 with the initial condition: x(t) =z (t) for t ≤ 0. We will
be interested  particularly in the
topological properties of emission and zone of emission.




Kaynakça

  • J. P. Aubin, A. Cellina; Differential inclusions, Springer-Verlag, 1984.
  • C. Berge; Espaces topologiques, fonctions set-valueds, Dunod, Paris, 1966.
  • L. Boudjenah; Existence of the solutions of the paratingent equation with delayed argument. Electron. J. Diff. Eqns., Vol. 2005, No.14, 1-8, 2005.
  • L Boudjenah; On the properties of the set solutions of a class of paratingent equation with delay. British Journal of Mathematics & Computer Science 4 (14): 1999-2003, 2014.
  • E. Campu; Equations diff´erentielles au paratingent `a retardement, dans les espaces de Banach. Th´eoreme d’existence des solutions. Rev. Roum. Math. Pures Appl. 20, 631-657 ,1975.
  • E, Campu ; Approximation des solutions des ´equations diff´erentielles au paratingent `a retardement, dans les espaces de Banach. Rev. Roum. Math. Pures Appl. 25, 509-518,1980.
  • C. Castaing, A. G. Ibrahim; Functional differential inclusions on closed sets in Banach spaces. Adv. Math. Eco. 2, 21-39, 2000.
  • K. Deimling; Multivalued differential equations, De Gruyter Ser. Nonlinear Anal. Appl. 1, Walter de Gruyter, Berlin, New York, 1992.
  • H.Frankowska, F.Rampazzo ; Filippov’s and Filippov-Wasewski theorems on closed domains. J. Diff. Equ, 161, 449-478, 2000.
  • G. Haddad; Monotone trajectories of differential inclusions and functional differential inclusions with memory, Israel J. Math. 39(1-2), 83-100. 1982.
  • G. Haddad; Monotone viable trajectories for functional differential inclusions with memory. J. Diff. Eq. 42, 1-24, 1981.
  • G. Haddad; Functional viability theorems for functional differential inclusions with memory. Ann. Inst. Henri Poincar´e I (3), 179-204, 1984.
  • G. Haddad, J. M. Lasry; Periodic solutions of functional differential inclusions and fixed points of -selectionable correspondences. J. Math. Anal. Appl. 96, 295-312, 1993.
  • M. Hukuhara; Sur l’application semi-continue dont la valeur est un compact convexe. RIMS-11, Res. Inst. Math. Sci. Kyoto. Univ. 941-945, 1963.
  • M. Kamenskii, V.Obukhovskii, P. Zecca; Condensing multivalued maps and semilinear differential inclusions in Banach spaces, De Gruyter Ser. Nonlinear Anal. Appl. 7, Walter de Gruyter, Berlin, New York, 2001.
  • M. Kisielewicz; Differential Inclusions and Optimal Control. Kluwer, Dordrecht, The Netherlands, 1991.
  • B. Kryzowa; Equation au paratingenta argument retard´e. Ann. Univ. Marie Curie-Sklodwska. Sectio A, 17, 7-18, 1965. B. Kryzowa; Sur les familles de solutions des ´equation au paratingenta argument retarde. Ann. Univ. Marie Curie-Sklodwska. Sectio A, 17, 19-24, 1965.
  • A. D. Myshkis; General theory of differential equations with delayed argument, Uspehi Matem. Nauk 4, no. 5, 1949, 99-141 (in Russian)
  • S. Raczynski; Differential inclusions in system simulation. Trans. Society for Computer Simulation, Vol. 13. No. 1, 47-54. 1996.
  • S. Raczynski; A market model: uncertainty and reachable sets. Int. J. Simul. Multisci. Des. Optim. 6, A2, 2015.
  • S. Raczynski; Creating galaxies on a PC. Simulation, Vol 74, No. 3, 161-166, 2000.
  • G. V. Smirnov; Introduction to the theory of differential inclusions, Amer. Math. Soc., Providence, R.I. 2002.
  • E.D Sontag; An infinite-time relaxation theorem for differential inclusions. in Proc. Amer.Math. Soc., V 131, N◦ 2, 487-499, 2001.
  • E.D Sontag ; A relaxation theorem for differential inclusions with applications to stability properties. in Mathematical Theory of Networks and Systems (D. Gilliam and J. Rosenthal, eds.), 12 pages, August 2002, Electronic Proceedings of MTNS-2002.
  • A. Syam; Contribution a letude des inclusion differentielles. Doctorat Thesis, Universite Montpellier II, 1993.
  • A. Turowicz; Sur les trajectoires et les quasitrajectoires des systemes de commande nonlineaires. Bull. Acad. Polon. Ser. Sci. Math., Astr., Phys, Vol 10, 529-531, 1963.
  • T. Wasewski; Sur une generalisation de la notion des solutions dune equation au contingent. Bull. Acad. Pol. Sci. Ser. Math. Astronom. Physi. 10 No. 1. Warszawa, 1962.
  • T. Wasewski; Sur les syst`emes de commande non lineaires dont le contredomaine n’est pas forcement convexe. Bull. Acad. Pol. Sci. Ser. Math. Astronom. Physi. 10 No. 1. Warswa. 1962.
  • T.Wazewski; Sur un systeme de commande dont les trajectoires coincident avec les quasitrajectoires d’un syst`eme de commande donn´e. Bull. Acad. Pol. Sci. Ser. Math., Astronom., Physi. 11, N◦ 3. Warszawa 1963.
  • W. Zygmunt; On a certain pratingent equation with a deviated argument. Ann. Univ. Marie. Curie-Sklodwska. Lublin. Polonia. 18, 14, 127-135, 1974.
  • W. Zygmunt; On some properties of a certain family of solutions of the paratingent equation. Ann. Univ.Marie Curie-Sklodowska, Lublin. Polonia. Sect. A -28, 136-141,1976.
Toplam 31 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Lotfi Boudjenah Bu kişi benim

Yayımlanma Tarihi 1 Mart 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 2

Kaynak Göster

APA Boudjenah, L. (2016). On the structure of the set solutions of a class of paratingent equation with delayed argument. New Trends in Mathematical Sciences, 4(2), 174-179.
AMA Boudjenah L. On the structure of the set solutions of a class of paratingent equation with delayed argument. New Trends in Mathematical Sciences. Mart 2016;4(2):174-179.
Chicago Boudjenah, Lotfi. “On the Structure of the Set Solutions of a Class of Paratingent Equation With Delayed Argument”. New Trends in Mathematical Sciences 4, sy. 2 (Mart 2016): 174-79.
EndNote Boudjenah L (01 Mart 2016) On the structure of the set solutions of a class of paratingent equation with delayed argument. New Trends in Mathematical Sciences 4 2 174–179.
IEEE L. Boudjenah, “On the structure of the set solutions of a class of paratingent equation with delayed argument”, New Trends in Mathematical Sciences, c. 4, sy. 2, ss. 174–179, 2016.
ISNAD Boudjenah, Lotfi. “On the Structure of the Set Solutions of a Class of Paratingent Equation With Delayed Argument”. New Trends in Mathematical Sciences 4/2 (Mart 2016), 174-179.
JAMA Boudjenah L. On the structure of the set solutions of a class of paratingent equation with delayed argument. New Trends in Mathematical Sciences. 2016;4:174–179.
MLA Boudjenah, Lotfi. “On the Structure of the Set Solutions of a Class of Paratingent Equation With Delayed Argument”. New Trends in Mathematical Sciences, c. 4, sy. 2, 2016, ss. 174-9.
Vancouver Boudjenah L. On the structure of the set solutions of a class of paratingent equation with delayed argument. New Trends in Mathematical Sciences. 2016;4(2):174-9.