EXISTENCE AND UNIQUENESS OF GREEN FUNCTION AND IT’S APPLICATION TO BOUNDARY VALUE PROBLEMS; CASE STUDY OF BESSEL OPERATOR OF ORDER “n”
ELVIS K. DONKOH *
Department of Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, Ghana
SAMUEL G. APAU
Department of Healthcare Management, Boitekanelo College, Botswana
KOFI A. ABABIO
Department of Mathematics and Statistics, Technical University of Kumasi (KT’sU), Ghana
*Author to whom correspondence should be addressed.
Abstract
In mathematical physics, certain initial value problems (IVP) and boundary value problems ( BVP) are better solved using Green function. The Bessel operator of order ‘n’ is a classical example. We prove the existence and uniqueness of such Green function; the results obtained uniquely will be used to solve the well known Bessel operator of non-zero order ‘n’ subject to the end conditions (0)=y(1)=0.
Keywords: Bessel operator, green function, integral equations, boundary value problem, existence and uniqueness