Volume 3,  Issue 2, 2002

Article 30

ON A NONCOERCIVE SYSTEM OF QUASI-VARIATIONAL INEQUALITIES RELATED TO STOCHASTIC CONTROL PROBLEMS

1M. BOULBRACHENE, 2M. HAIOUR AND 1B. CHENTOUF

1SULTAN QABOOS UNIVERSITY, 
COLLEGE OF SCIENCE, 
DEPARTMENT OF MATHEMATICS &
STATISTICS, 
P.O. BOX 36 MUSCAT 123, 
SULTANATE OF OMAN.
E-Mail: boulbrac@squ.edu.om

2DEPARTEMENT DE MATHEMATIQUES, 
FACULTE DES SCIENCES, 
UNIVERSITE DE ANNABA,
B.P. 12 ANNABA 23000 ALGERIA.
E-Mail: haiourmed@caramail.com

E-Mail: chentouf@squ.edu.om

Received 29 October, 2001; Accepted 11 February, 2002.
Communicated by: R. Verma

ABSTRACT.   This paper deals with a system of quasi-variatioan inequalities with noncoercive operators. We prove the existence of a unique weak solution using a lower and upper solutions approach. Furthermore, by means of  a Banach's fixed point approach, we also prove that the standard finite element approximation applied to this system is quasi-optimally accurate in L¥.
Key words:
Quasi-variational inequalities, Contraction, Fixed point finite element, Error estimate.

2000 Mathematics Subject Classification:
49J40, 65N30, 65N15.

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