MAXIMUM PRINCIPLE AND NONLINEAR THREE POINT SINGULAR BOUNDARY VALUE PROBLEMS ARISING DUE TO SPHERICAL SYMMETRY

摘要

We consider the following class of nonlinear three point singular boundary value problems (SBVPs)-y"(x)-(2/x)y'(x)=f(x,y),0＜x＜l, y'(0) = 0,y(1) = δy(η), where δ ＞ 0 and 0 ＜ η ＜ 1. We establish some new maximum principles. Further using these maximum principles and monotone iterative technique in the presence of upper and lower solution we prove existence of solutions for the above class of nonlinear three point SBVPs. Here the nonlinear term is one sided Lipschitz continuous in its domain, also x = 0 is regular singular point of the above differential equation.