REDUCTION OF AN OPERATOR EQUATION IN TO AN EQUIVALENT BIFURCATION EQUATION THROUGH SCHAUDERS FIXED POINT THEOREM

In this paper we deal with the Nonlinear Coupled Ordinary Dif- ferential Equations(Nonlinear CODE). A Multipoint Boundary Value Prob- lem(MBVP) associated with these Nonlinear Equations is deflned as an Oper- ator Equation. This equation(inflnite dimensional) is reduced to an Equivalent Bifurcation Equation(flnite dimensional) using Schauder's Fixed Point Theo- rem. This Bifurcation Equation being on a flnite dimensional space can be easily solved by using standard approximation techniques.