Positive Solutions for a Class of Nonlinear Boundary Value Problems with Neumann]Robin Boundary Conditions

We consider the two point boundary value problem yu0 x.slf u x..; 0-x-1 u9 0. s0; u9 1. qa u 1. s0 where l )0 and a )0 are parameters, and fgC2w0, 1x. We discuss the existence of nonnegative solutions for superlinear nonlinearities by developing a quadrature method. We study the positone f 0.)0. case as well as the semipositone f 0.-0. case, and note a drastic difference in the respective bifurcation diagrams for positive solutions