Positive Solutions for Quasilinear Second Order Differential Equation

It is well known that Krasnose´skii fixed point theorem is very important. It was extensively used for studying the boundary value problems. In this paper, Krasnose´skii fixed point theorem is extended. A new fixed point theorem is obtained. The second order quasilinear differential equation (Phi(y´))´ + a(t)f(t,y,y´) = 0, 0 < t < 1 subject to Dirichlet boundary condition is studied, where f is a non-negative continuous function, Phi(v) = |v|^p-2v, p > 1. We show the existence of at least one positive solution by using the new fixed point theorem in cone.