Department of Mathematics, Eritrea Institute of Technology, Mainefhi, Eritrea
AMS MSC: 34B18, 34B99, 35J05
In this article a more generalized four point boundary value problem associated with a third order differential equation involving mixed boundary conditions is proposed. First we constructed the Green's function for the associated third order three point boundary value problem through undetermined parametric method and then the idea is extended to the third order four point boundary value problem with mixed boundary conditions. Using this idea and an Iteration method is proposed to solve the corresponding nonlinear problem.
Green's function, Schauder fixed point theorem, Vitali's convergence theorem