PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

An existence result for hyperbolic functional differential inclusions

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we investigate the existence of solutions on an unbounded domain to an hyperbolic differential inclusion in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension to multivalued on locally convex topological spaces, of Schaefer's theorem.
Twórcy
autor
  • Department of Mathematics, University of Sidi Bel Abbes, BP 89 2000 Sidi Bel Abbes, Algeria
  • Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Bibliografia
  • [1] J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, Marcel-Dekker, New York, 1980.
  • [2] M. Benchohra and S. K. Ntouyas, On an hyperbolic functional differential inclusion in Banach spaces, preprint.
  • [3] M. Benchohra and S. K. Ntouyas, Hyperbolic functional differential inclusions in Banach spaces with nonlocal conditions, Funct. Approx. Comment. Math. 29 (2001), 29-39.
  • [4] S. Brzychczy and J. Janus, Monotone iterative method for nonlinear hyperbolic differential functional equations, Univ. Iagel. Acta Math. 37 (1999), 245-261.
  • [5] T. Człapiński, Existence of solutions of the Darboux problem for partial differential functional equations with infinite delay in a Banach space, Comment. Math. Prace Matem. 35 (1995), 111-122.
  • [6] T. Człapiński, Difference methods for the Darboux problem for functional partial differential equations, Ann. Polon. Math. 71 (1999), 171-193.
  • [7] T. Człapiński, Iterative methods for the Darboux problem for partial functional differential functional equations, J. Inequal. Appl. 4 (1999), 141-161.
  • [8] T. Człapiński, On the Chaplyghin method for partial differential functional equations of the first order, Univ. Iagel. Acta Math. 35 (1997), 137-149.
  • [9] F. De Blasi and J. Myjak, On the structure of the set of solutions of the Darboux problem for hyperbolic equations, Proc. Edinburgh Math. Soc. 29 (1986), 7-14.
  • [10] F. DeBlasi and J. Myjak, On the set of solutions of a differential inclusion, Bull. Inst. Math., Acad. Sin. 14 (1986), 271-275.
  • [11] K. Deimling, Multivalued Differential Equations, Walter de Gruyter, Berlin-New York, 1992.
  • [12] Z. Denkowski and A. Pelczar, On the existence and uniqueness of solutions of some partial differential functional equations, Ann. Polon. Math. 35 (1978), 261-304.
  • [13] L. Górniewicz, Topological fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht, 1999.
  • [14] S. Heikkila and V. Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker, New York, 1994.
  • [15] Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Vol. I; Theory, Kluwer Academic, Dordrecht, Boston, London, 1997.
  • [16] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Mathematics and Applications 486, Dordrecht, 1999.
  • [17] Z. Kamont, On the Chaplyghin method for partial differential functional equations of the first order, Ann. Polon. Math. 38 (1980), 313-324.
  • [18] Z. Kamont, Finite difference approximations for first order partial differential functional equations, Ukrain. Math. J. 46 (1994), 265-287.
  • [19] I. Kubiaczyk, Kneser’s theorem for hyperbolic equations, Funct. Approx. Comment. Math. 14 (1984), 183-196.
  • [20] A. Lasota and Z. Opial, 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.
  • [21] T. W. Ma, Topological degrees for set-valued compact vector fields in locally convex spaces, Dissertationess Math. 92 (1972), 1-43.
  • [22] N. S. Papageorgiou, Existence of solutions for hyperbolic differential inclusions in Banach spaces, Arch. Math. (Brno) 28 (1992), 205-213.
  • [23] A. Pelczar, Some functional differential equations, Dissertationes Math. 100 (1973), 3-110.
  • [24] H. Schaefer, Uber die methode der a priori schranken, Math. Ann. 129, (1955), 415-416.
  • [25] K. Yosida, Functional Analysis, 6th edn. Springer-Verlag, Berlin, 1980.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0002-0042
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.