Ten serwis zostanie wyłączony 2025-02-11.
Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl

PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2012 | Vol. 45, nr 1 | 67-79
Tytuł artykułu

Existence of solutions for some nonlinear delay integrodifferential equations with nonlocal initial conditions

Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The main purpose of this paper is the existence of mild solutions for a class of first-order nonlinear delay integrodifferential equations with nonlocal initial conditions in Banach spaces. We show that the solutions are given by the application of the theory of resolvent operators and the Sadovskii's fixed point theorem. An example is presented in the end to show the applications of the obtained results.
Wydawca

Rocznik
Strony
67-79
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
Bibliografia
  • [1] S. Aizicovici, H. Lee, Nonlinear nonlocal Cauchy problems in Banach spaces, Appl. Math. Lett. 18 (2005), 401–407.
  • [2] L. Byszewski, V. Lakshmikantham, Theorem about existence and uniqueness of a solutions of a nonlocal Cauchy problem in a Banach space, Appl. Anal. 40 (1990), 11–19.
  • [3] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494–505.
  • [4] L. Byszewski, Existence and uniqueness of solutions of semilinear evolution nonlocal Cauchy problem, Zeszyty Nauk. Politech. Rzeszowskiej Mat. Fiz. 18 (1993), 109–112.
  • [5] L. Byszewski, H. Akca, Existence of solutions of a semilinear functional-differential evolution nonlocal problem, Nonlinear Anal. 34 (1998), 65–72.
  • [6] M. Benchohra, E. Gatsori, J. Henderson, S. K. Ntouyas, Nondensely defined evolution impulsive differential inclusions with nonlocal conditions, J. Math. Anal. Appl. 286 (2003), 307–325.
  • [7] K. Balachandran, J. Y. Park, M. Chandrasekaran, Nonlocal Cauchy problems for delay integrodifferential equations of Sobolev type in Banach spaces, Appl. Math. Lett. 15 (2002), 845–854.
  • [8] K. Deng, Exponential decay of solutions of semilinear parabolic equations with non-local initial conditions, J. Math. Anal. Appl. 179 (1993), 630–637.
  • [9] X. Fu, K. Ezzinbi, Existence of solutions for neutral functional differential evolution equations with nonlocal conditions, Nonlinear Anal. 54 (2003), 215–227.
  • [10] R. Grimmer, J. H. Liu, Integrated semigroups and integrodifferential equations, Semi-group Forum 48 (1994), 79–95.
  • [11] R. Grimmer, Resolvent operators for integral equations in Banach space, Trans. Amer. Math. Soc. 48 (1982), 333–349.
  • [12] R. R. Kumar, Nonlocal Cauchy problem for analytic resolvent integrodifferential equations in Banach spaces, Appl. Math. Comput. 204 (2008), 352–362.
  • [13] J. H. Liu, Resolvent operators and weak solutions of integrodifferential equations, Differential Integral Equations 7 (1994), 523–534.
  • [14] Y. Lin, J. H. Liu, Semilinear integrodifferential equations with nonlocal Cauchy problem, Nonlinear Anal. 26 (1996), 1023–1033.
  • [15] J. Liang, J. H. Liu, T. J. Xiao, Nonlocal Cauchy problems governed by compact operator families, Nonlinear Anal. 57 (2004), 183–189.
  • [16] S. K. Ntouyas, P. Ch. Tsamatos, Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl. 210 (1997), 679–687.
  • [17] B. N. Sadovskii, On a fixed point principle, Funct. Anal. Appl. 1 (1967), 74–76.
  • [18] J. Pruss, On resolvent operators for linear integrodifferential equations of Volterra type, J. Integral Equations 5 (1983), 211–236.
  • [19] K. Yosida, Functional Analysis, 6th ed., Springer, Berlin, 1980.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0034-0008
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.