A multiplicity result for a singular generalized Sturm-Liouville boundary value problem
In this paper, we are concerned with a singular generalized Sturm-Liouville boundary value problem {u ''(t) + h(t)f(t, u(t), u'(t)) = 0, 0 < t < 1, au(0) - bu'(0) = Sigma(m-2)(i=1)a(i)u(xi(i)), cu(1) + du'(1) = Sigma(m-2)(i=1)b(i)u(xi(i)), where h may be singular at t = 0 and/or t = 1. By applying the fixed point theorem in cones, a new and general result on the existence of positive solutions to the second order singular generalized Sturm-Liouville boundary value problem is obtained. The first order derivative is involved in the nonlinear term f explicitly. (C) 2009 Elsevier Ltd. All rights reserved.
singular fixed point cone positive solution generalized sturm-liouville problem