Publication Cover
Applicable Analysis
An International Journal
Volume 85, 2006 - Issue 10
57
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Extrapolation spaces and controllability of impulsive semilinear functional differential inclusions with infinite delay in Fréchet spaces

&
Pages 1255-1270 | Received 06 Jan 2006, Accepted 25 May 2006, Published online: 04 Jan 2007

References

  • Ahmed , NU . 1991 . Semigroup Theory with Applications to Systems and Control , Vol. 246 , London, New York : Longman Scientific and Technical and John Wiley .
  • Amann , H . 1995 . Linear and Quasilinear Parabolic Problems , Berlin : Birkhäuser .
  • Amir , B and Maniar , L . 1998 . Application de la théorie d'extrapolation pour la résolution des équations différentielles á retard homogénes. . Extracta Mathematica , 13 : 95 – 105 .
  • Bainov , DD and Simeonov , PS . 1989 . Systems with Impulse Effect , Chichester : Ellis Horwood Ltd. .
  • Balachandran , K and Manimegalai , P . 2002 . Controllability of nonlinear abstract neutral evolution integrodifferential systems. . Nonlinear Functional Analysis Applications , 7 : 85 – 100 .
  • Benchohra , M , Gatsori , EP , Górniewicz , L and Ntouyas , SK . 2003 . Controllability results for evolutioninclusions with non-local conditions. . Zeitschrift Für Analysis and Anwendungen , 22 : 411 – 431 .
  • Benchohra , M , Górniewicz , L , Ntouyas , SK and Ouahab , A . 2004 . Controllability results for impulsivefunctional differential inclusions. . Reports on Mathematical Physics , 54 : 211 – 227 .
  • Benchohra , M , Górniewicz , L , Ntouyas , SK and Ouahab , A . 2003 . “ Existence results for nondensely defined impulsive semilinear functional differential equations ” . In Nonlinear Analysis and Applications , Edited by: Agarwal , RP and O'Regan , D . Dordrecht : Kluwer .
  • Benchohra , M , Henderson , J , Ntouyas , SK and Ouahab , A . 2006 . Boundary value problems for impulsive functional differential equations with infinite delay. . International Journal of Mathematics and Computer Science , 1 : 27 – 39 .
  • Benchohra , M and Ntouyas , SK . 2003 . Existence and controllability results for multivalued semilinear differential equations with nonlocal conditions. . Soochow Journal of Mathematics , 29 : 157 – 170 .
  • Benchohra , M and Ouahab , A . 2005 . Controllability results for functional semilinear differential inclusionsin Fréchet Spaces. . Nonlinear Analysis , 61 : 405 – 423 .
  • Benchohra , M , Ntouyas , SK and Górniewicz , L . 2003 . Controllability of Some Nonlinear Systems in Banach Spaces (The Fixed Point Theory Approach) , Plock : Plock University Press .
  • Castaing , C and Valadier , M . 1977 . Convex Analysis and Measurable Multifunctions , Vol. 580 , Berlin-Heidelberg-New York : Springer-Verlag . . Lecture Notes in Mathematics
  • Corduneanu , C and Lakhmikantham , V . 1980 . Equations with unbounded delay . Nonlinear Analysis , 4 : 831 – 877 .
  • Da Prato , G and Grisvard , E . 1982 . On extrapolation spaces. . Rendiconti Accademia Nazionnale Lincei , 72 : 330 – 332 .
  • Da Prato , G and Sinestrari , E . 1987 . Differential operators with non-dense domains. . Annali della Scuda Scuola Normale Superiore di Pisa , 14 : 285 – 344 .
  • Deimling , K . 1992 . Multivalued Differential Equations , Berlin-New York : De Gruyter .
  • Engel , KJ and Nagel , R . 2000 . One-Parameter Semigroups for Linear Evolution Equations , New York : Springer-Verlag .
  • Ezzinbi , K . 2003 . Existence and stability for some partial functional differential equations with infinite delay. . Electronic Journal of Differential Equations , 2003 : 1 – 13 .
  • Frigon , M . 2002 . Fixed point results for multivalued contractions on gauge spaces, set valued mappings with applications in nonlinear analysis. . Series Mathematical Analysis and Applications , 4 : 175 – 181 .
  • Górniewicz , L . 1999 . “ Topological Fixed Point Theory of Multivalued Mappings ” . In Mathematics and its Applications , 495 Dordrecht : Kluwer Academic Publishers .
  • Graef , JR and Ouahab , A . “ Some existence results and uniqueness solutions for functional impulsive differential equations with variable times in Fréchet Spaces ” . In Dynamics of Continuous, Discrete & Impulsive Systems in press
  • Guhring , G , Rabiger , F and Ruess , W . 2000 . Linearized stability for semilinear non-autonomous evolutionequations to retarded differential equations. . Differential and Integral Equations , 13 : 503 – 527 .
  • Guo , G . 2002 . A class of second-order impulsive integro-differential equations on unbounded domain ina Banach space. . Applied Mathematics and Computation , 125 : 59 – 77 .
  • Hale , J and Kato , J . 1978 . Phase space for retarded equations with infinite delay. . Funkcialaj Ekvacioj , 21 : 11 – 41 .
  • Hale , JK . 1987 . “ Retarded equations with infinte delay ” . In Functional and Approximation of Fixed Points Proceedings, Bonn, Lecture Notes in Mathematics , Vol. 1223 , 61 – 63 . Berlin : Springer .
  • Hale , JK . 1988 . Asymptotic Behavior of Disspative Systems , Providence, RI : American Mathematical Society .
  • Hale , JK and Lunel , SMV . 1993 . “ Introduction to Functional Differential Equations ” . In Applied Mathematical Sciences , Vol. 99 , New York : Springer-Verlag .
  • Henderson , J and Ouahab , A . 2005 . Existence results for nondensely defined semilinear functional differentialinclusions in Fréchet spaces. . Electronic Journal of the Qualitative Theory of Differential Equation , 11 : 1 – 17 .
  • Henderson , J and Ouahab , A . 2005 . Global existence results for impulsive functional differential inclusionswith multiple delay in Fréchet Spaces. . PanAmerican Mathematical Journal , 15 : 73 – 89 .
  • Hino , Y , Murakani , S and Naito , T . 1991 . Functional Differential Equations with Infinite Delay , Vol. 1473 , Berlin : Springer-Verlag . . In: Lecture Notes in Mathematics
  • Hu , S and Papageorgiou , N . 1997 . Handbook of Multivalued Analysis, Volume I: Theory , Dordrecht : Kluwer .
  • Kamenskii , M , Obukhovskii , V and Zecca , P . 2001 . Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces , Berlin : Walter de Gruyter & Co. .
  • Kappel , F and Schappacher , W . 1980 . Some considerations to the fundamental theory of infinite delay equations. . Journal of Differential Equations , 37 : 141 – 183 .
  • Lakshmikantham , V , Bainov , DD and Simeonov , PS . 1989 . Theory of Impulsive Differential Equations , Singapore : World Scientific .
  • Lakshmikantham , V , Wen , L and Zhang , B . 1994 . “ Theory of Differential Equations with Unbounded Delay ” . In Mathematics and its Applications , Dordrecht : Kluwer Academic Publishers .
  • Li , G and Xue , X . 2003 . Controllability of evolution inclusions with nonlocal conditions. . Applied Mathematics and Computation , 141 : 375 – 384 .
  • Nagel , R and Sinestrari , E . 1998 . “ Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators ” . In Functional Analysis , Edited by: Bierstedt , KD , Pietsch , A , Ruess , WM and Voigt , D . 51 – 70 . New York : Marcel Dekker .
  • Neerven , J . 1992 . The Adjoint of a Semigroup of Linear Operators Lecture Notes in Mathematics , 1529 NewYork : Springer-Verlag .
  • Nickel , G and Rhandi , A . “ On the essential spectral radius of semigroups generated by pertubations of Hille-Yosida operators ” . In Differential Integral Equations in press
  • Ouahab , A . “ Local and global existence and uniqueness results for impulsive differential equtions with multiple delay ” . In Journal of Mathematical Analysis Applications in press
  • Pazy , A . 1983 . Semigroups of Linear Operators and Applications to Partial Differential Equations , NewYork : Springer-Verlag .
  • Quinn , MD and Carmichael , N . 1984–85 . An approach to nonlinear control problem using fixed point methods, degree theory, pseudo-inverses . Numerical Functional Analysis and Optimization , 7 : 197 – 219 .
  • Samoilenko , AM and Perestyuk , NA . 1995 . Impulsive Differential Equations , Singapore : World Scientific .
  • Schumacher , K . 1978 . Existence and continuous dependence for differential equations with unbounded delay. . Archive for Rational Mechanics and Analysis , 64 : 315 – 335 .
  • Sawano , K . 1982 . Some considerations on the fundamental theorems for functional differential equationswith infinite delay. . Funkcial. Ekvac. , 25 : 97 – 104 .
  • Shin , JS . 1987 . An existence of functional differential equations with infinite delay in a Banach space . Funkcial. Ekvac , 30 : 19 – 29 .
  • Tolstonogov , AA . 2000 . Differential Inclusions in a Banach Space , Dordrecht : Kluwer .
  • Yosida , K . 1980 . Functional Analysis , 6th , Berlin : Springer-Verlag .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.