ON THE BOUNDED AND UNIQUE SOLVABILITY OF THE BOUNDARY VALUE PROBLEM OF THE EQUATION IN THE SPACE OF SCALAR FUNCTIONS WITH ABSOLUTE CONTINUOUS DERIVATIVE OF THE (n -1) ORDER AND ITS ISOTONIC GREEN OPERATOR FOR A CERTAIN CLASS OF LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS
EBIENDELE EBOSELE PETER *
Department of Basic Science, School of General Studies, Federal Polytechnic, Auchi, Edo State, Nigeria.
ALIU MOMOH AGWELI
Department of Basic Science, School of General Studies, Federal Polytechnic, Auchi, Edo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The objectives of this paper is to investigate the boundary value problem of the equation in the space of scalar functions with absolute continuous derivative of the nth order, and to establishes the effective and sufficient conditions for its bounded and it unique Solvability. Theorems were stated and prove under the Preliminaries note, about four Theorems with applications to prove the main results. The necessary and sufficient conditions that guarantee the studied boundary value problem to satisfy the Isotonic Property of the Green Operator was also established. My approach in this study improved on the literatures, to the case where more than two arguments of the studying equations were established, as in the case of one argument in the authors in [3,4].
Keywords: Bounded, boundary value problem, continuous derivative, green operator, solvability