Existence and controllability results for nonlinear differential inclusions with nonlocal conditions in Banach spaces

• Autorzy: Benchohra M. , Ntouyas S. K.
• Języki publikacji: EN

Abstrakty

EN

In this paper we investigate the existence and controllability of mild solutions to the first order semilinear evolution inclusions in Banach spaces with nonlocal conditions. We shall rely of a fixed point theorem for condensing maps due to Martelli.

Słowa kluczowe

EN

nonlocal condition; convex multivalued map; mild solution; evolution inclusion; controllability; fixed point

PL

nielokalny warunek; wypukłe odwzorowanie wielowartościowe; łagodne rozwiązanie; inkluzja rozwoju; zdolność sterowania(sterowanie); punkt stały

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2002
• Tom: Vol. 8, nr 1
• Strony: 33--48
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Benchohra M.

• Department of Mathematics University of Sidi Bel Abbes BP 89, 22000 Sidi Bel Abbes Algeria

autor

Ntouyas S. K.

• Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Bibliografia

• [1] Anguraj, A., Balachandran, K., Existence of solutions of nonlinear differential inclusions, Mem. Fac. Sci. Kochi Univ. Ser. A Math. 13 (1992), 61-66.
• [2] Balachandran, K., Balasubramaniam, P., Dauer, J. P., Controllability of nonlinear integrodifferential systems in Banach space, J. Optim. Theory Appl. 84 (1995), 83- 91.
• [3] Balachandran, K., Ilamaran, S., Existence and uniqueness of mild and strong solutions of a semilinear evolution equation with nonlocal condition, Indian J. Pure Appl. Math. 25(4) (1994), 411-418.
• [4] Balachandran, K., Chandrasekaran, M., Existence of solutions of a delay differential equation with nonlocal condition, Indian J. Pure Appl. Math. 27(5) (1996), 443-449.
• [5] Banas, J., Goebel, K., Measures of Noncompactness in Banach Spaces, Marcel-Dekker, New York, 1980.
• [6] Byszewski, L., Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494-505.
• [7] Byszewski, L., Existence and uniqueness of mild and classical solutions of semilinear functional differential evolution nonlocal Cauchy problem, Sel. Problems Math., Cracow University of Technology, Anniversary Issue 6 (1995), 25-33.
• [8] Darbo, G., Punti uniti in trasformazioni a codominio non-compacto Rend. Sem. Mat. Univ. Padova 24 (1955), 353-367.
• [9] Deimling, K., Multivalued Differential Equations, Walter de Gruyter, Berlin-New York, 1992.
• [10] Hale, J. K., Ordinary Differential Equations, Interscience, New York, 1969.
• [11] Han, H. K., Park, J. Y., Boundary controllability of differential equations with non-local condition, em J. Math. Anal. Appl. 230 (1999), 241-250.
• [12] Hu, S., Papageorgiou, N., Handbook of Multivalued Analysis, Volume I: Theory, Kluwer, Dordrecht, Boston, London, 1997.
• [13] Lasota, A., Opial, Z., An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations, Bull. Polish Acad. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786.
• [14] Marino, G., Nonlinear boundary value problems for multivalued differential equations in Banach spaces, Nonlinear Anal. 14(1990), 545-558
• [15] Martelli, M., A Rothe’s type theorem for non-compact acyclic-valued map, Boll. Un. Mat. Ital. 11 (1975), 70-76.
• [16] Ntouyas, S. K., Tsamatos, P. Ch., Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl. 210 (1997), 679-687.
• [17] Yosida, K., Functional Analysis, 6th ed., Springer-Verlag, Berlin, 1980.