Boundary value problem for a class of nonlinear second order ordinary differential equations with variable coefficients

Abstract

In this article the existence of continuous solutions of two-point boundary value problem in an interval of positive real line for a class of nonlinear second order ordinary differential equations with variable coefficients is proved. To prove of the existence theorem about two-point boundary value problem the authors constructed the general solution of the corresponding linear second order differential equations with variable coefficients and used Schauder fixed point principle. The method of building of the solution of linear second order differential equations with variable coefficients and the general solution can be useful for various applications of science. For simplicity the coefficient and the nonlinear part of the ordinary second order differential equation are taken from the class of continuous functions. They can be taken from the class of measurable and essentially bounded functions. One can easily verify that the results remain in force and in this case.