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

• Autorzy: Mouffak Benchohra
• 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.

Słowa kluczowe

EN

initial value problems; convex multivalued map; mild solution; evolution inclusion; existence; fixed point; abstract space

Kategorie tematyczne

• 34A60: Differential inclusions
• 34G20: Nonlinear equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1999
• Tom: 19
• Numer: 1-2
• Strony: 111-121

Daty

wydano

1999

otrzymano

1999-08-12

Twórcy

autor

Mouffak Benchohra

• 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.