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 Differential Equations(Nonlinear CODE). A Multipoint Boundary Value Problem(MBVP) associated with these Nonlinear Equations is defined as an Oper- ator Equation. This equation(infinite dimensional) is reduced to an Equivalent Bifurcation Equation(finite dimensional) using Schauder s Fixed Point Theorem. This Bifurcation Equation being on a finite dimensional space can be easily solved by using standard approximation techniques.