The existence of positive solutions for some nonlinear boundary value problems with linear mixed boundary conditions

In this paper we study the existence of positive solutions of the equation ϕ(x ) + a(t)f x(t) = 0, where ϕ :R →R is an increasing homeomorphism and homomorphism and ϕ(0) = 0, subject to linear mixed boundary conditions by a simple application of a fixed point index theorem in cones.  2005 Elsevier Inc. All rights reserved.