Volume 3,  Issue 1, 2002

Article 14

LOWER AND UPPER SOLUTIONS METHOD FOR FIRST ORDER DIFFERENTIAL INCLUSIONS WITH NONLINEAR BOUNDARY CONDITIONS

M. BENCHOHRA AND S.K. NTOUYAS

DEPARTEMENT DE MATHEMATIQUES, 
UNIVERSITE DE SIDI BEL ABBES, 
BP 89, 22000 SIDI BEL ABBES, 
ALGERIE
E-Mail: benchohra@yahoo.com

Received  17 May, 2001; Accepted 29 October, 2001.
Communicated by: B.G. Pachpatte

ABSTRACT.   In this paper a fixed point theorem for condensing maps combined with upper and lower solution are used to investigate the existence of solutions of first order differential inclusions with general nonlinear boundary conditions.
Key words:
Initial value problem, Convex multivalued map, Differential inclusions, Nonlinear boundary conditions, Condensing map, Fixed point, Truncation map, Upper and lower solutions.

2000 Mathematics Subject Classification:
34A60.

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