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Global convergence of successive approximations of the Darboux problem for partial functional differential equations with infinite delay

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the Darboux problem for the hyperbolic partial functional differential equation with infinite delay. We deal with generalized (in the "almost everywhere" sense) solutions of this problem. We prove a theorem on the global convergence of successive approximations to a unique solution of the Darboux problem.
Rocznik
Strony
327--338
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
  • University of Gdansk Institute of Mathematics Wita Stwosza 57, 80-952 Gdansk, Poland
Bibliografia
  • 1] S. Abbas, M. Benchohra, Darboux problem for partial differential equations with infinite delay and Caputo’s fractional derivative, Adv. Dyn. Syst. Appl. 5 (2010), 1–19.
  • [2] S. Abbas, M. Benchohra, J.J. Nieto, Global uniqueness results for fractional order partial hyperbolic functional differential equations, Adv. Difference Equ. 2011, Article ID 379876, 25 pp. (2011).
  • [3] H.Y. Chen, Successive approximations for solutions of functional integral equations, J. Math. Anal. Appl. 80 (1981), 19–30.
  • [4] C. Corduneau, V. Lakshmikantham, Equations with unbounded delay: survey, Nonlinear Anal. 4 (1980), 831–877.
  • [5] T. Człapinski, Existence of solutions of the Darboux problem for partial differential-functional equations with infinite delay in a Banach space, Comm. Math. 35 (1995), 111–122.
  • [6] T. Człapinski, On the Darboux problem for partial differential-functional equations with infinite delay at derivatives, Nonlin. Anal. 44 (2001), 389–398.
  • [7] F.S. De Blasi, J. Myjak, Some generic properties of functional differential equations in Banach space, J. Math. Anal. Appl. 80 (1981), 19–30.
  • [8] L. Faina, The generic property of global covergence of successive approximations for functional differential equations with infinite delay, Comm. Appl. Anal. 3 (1999), 219–234.
  • [9] J.K. Hale, J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978), 11–41.
  • [10] Y. Hino, S. Murakami, T. Naito, Functional differential equations with infinite delay, Lect. Notes Math., 1473, Springer-Verlag, Berlin – Heidelberg – New York, 1991.
  • [11] F. Kappel, W. Schappacher, Some considerations to fundamental theory of infinite delay equations, J. Differential Equations 37 (1980), 141–183.
  • [12] J.S. Shin, Uniqueness and global convergence of successive approximations for solutions of functional integral equations with infinite delay, J. Math. Anal. Appl. 120 (1986), 71–88.
  • [13] J.S. Shin, Global convergence of successive approximations of solutions for functional differential equations with infinite delay, Tôhoku Math. J. 39 (1986), 557–574.
  • [14] K. Schumacher, Existence and continuous dependence for functional differential equations with infinite delay, Arch. Rational Mech. Anal. Appl. 7 (1978), 315–334.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-46bad550-3a54-49f3-846b-a2fd4dfe5d3c
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