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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.
Wydawca
Rocznik
Tom
Strony
1--16
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
- Department of Mathematics, University of Sidi Bel Abbes, BP 89 2000 Sidi Bel Abbes, Algeria
autor
- 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
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bwmeta1.element.baztech-article-BUS2-0002-0042