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Tytuł artykułu

An existence theorem for an hyperbolic differential inclusion in Banach spaces

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EN
Abstrakty
EN
In this paper, we investigate the existence of solutions on unbounded domain to a hyperbolic differential inclusion in Banach spaces. We shall rely on a fixed point theorem due to Ma which is an extension to multivalued between locally convex topological spaces of Schaefer's theorem.
Twórcy
  • Laboratory of Mathematics, University of Sidi Bel Abbès, BP 89, 22000 Sidi Bel Abbès, Algérie
  • Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Bibliografia
  • [1] L. Byszewski, Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation $u''_{xt} = F(x,t,u,u_x)$, J. Appl. Math. Stoch. Anal. 3 (3) (1990), 163-168.
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  • [3] L. Byszewski and V. Lakshmikantham, Monotone iterative technique for nonlocal hyperbolic differential problem, J. Math. Phys. Sci. 26 (4) (1992), 345-359.
  • [4] L. Byszewski and N.S. Papageorgiou, An application of a noncompactness technique to an investigation of the existence of solutions to nonlocal multivalued Darboux problem, J. Appl. Math. Stoch. Anal. 12 (2) (1999), 179-190.
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  • [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.
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  • [15] Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory, Kluwer, Dordrecht, Boston, London, 1997, Volume II: Applications, Kluwer, Dordrecht, Boston, London 2000.
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  • [17] I. Kubiaczyk and A.N. Mostafa, On the existence of weak solutions of the Darboux problem for the hyperbolic partial differential equations in Banach spaces, Fasc. Math. 28 (1998), 93-99.
  • [18] 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.
  • [19] T.W. Ma, Topological degrees for set-valued compact vector fields in locally convex spaces, Dissertationess Math. 92 (1972), 1-43.
  • [20] N.S. Papageorgiou, Existence of solutions for hyperbolic differential inclusions in Banach spaces, Arch. Math. (Brno) 28 (1992), 205-213.
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  • [22] K. Yosida, Functional Analysis, 6th edn. Springer-Verlag, Berlin 1980.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1029
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