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1999 | 19 | 1-2 | 111-121
Tytuł artykułu

Existence of mild solutions on infinite intervals to first order initial value problems for a class of differential inclusions in banach spaces

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we investigate the existence of mild solutions on an unbounded real interval to first order initial value problems for a class of differential inclusions in Banach spaces. We shall make use of a theorem of Ma, which is an extension to multivalued maps on locally convex topological spaces of Schaefer's theorem.
Twórcy
  • Département de Mathématiques, Université de Sidi Bel Abbes, BP 89, 22000 Sidi Bel Abbes, Algérie
Bibliografia
  • [1] E.P. Avgerinov and N.S. Papageorgiou, On quasilinear evolution inclusions, Glas. Mat. Ser. III 28 (48) No. 1 (1993), 35-52.
  • [2] M. Benchohra and A. Boucherif, An existence result on an unbounded real interval to first order initial value problems for differential inclusions in Banach spaces, Nonlinear Differential Equations, to appear.
  • [3] M. Benchohra and A. Boucherif, Existence of solutions on infinite intervals to second order initial value problems for a class of differential inclusions in Banach spaces, Dynamic Systems and Applications, to appear.
  • [4] K. Deimling, Multivalued Differential Equations, Walter de Gruyter, Berlin-New York 1992.
  • [5] M. Furi and P. Pera, A continuation method on locally convex spaces and applications to ordinary differential equations on noncompact intervals, Ann. Polon. Math. 47 (1987), 331-346.
  • [6] J.A. Goldstein, Semigroups of Linear Operators and Applications, Oxford, New York 1985.
  • [7] S. Heikkila and V. Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker, New York 1994.
  • [8] S. Heikkila and V. Lakshmikantham, On mild solutions of first order discontinuous semilinear differential equations in Banach spaces, Appl. Anal. 56 (1-2) (1995), 131-146.
  • [9] G. Ladas and V. Lakshmikantham, Differential Equations in Abstract Spaces, Academic Press, New York, London 1972.
  • [10] V. Lakshmikantham and S. Leela, Existence and monotone method for periodic solutions of first order differential equations, J. Math. Anal. Appl. 91 (1983), 237-243.
  • [11] 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.
  • [12] T.W. Ma, Topological degrees for set-valued compact vector fields in locally convex spaces, Dissertationess Math. 92 (1972), 1-43.
  • [13] R.H. Martin, Jr., Nonlinear perturbations of linear evolution systems, J. Math. Soc. Japan 29 (2) (1977), 233-252.
  • [14] N.S. Papageorgiou, Mild solutions of semilinear evolution inclusions, Indian J. Pure Appl. Math. 26 (3) (1995), 189-216.
  • [15] N.S. Papageorgiou, Boundary value problems for evolution inclusions, Comment. Math. Univ. Carol. 29 (1988), 355-363.
  • [16] H. Schaefer, Uber die methode der a priori schranken, Math. Ann. 129, (1955), 415-416.
  • [17] K. Yosida, Functional Analysis, 6^{th} edn. Springer-Verlag, Berlin 1980.
  • [18] S. Zaidman, Functional Analysis and Differential Equations in Abstract Spaces, Chapman & Hall/CRC, 1999.
Typ dokumentu
Bibliografia
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