Positive solutions for singular second order differential equations with integral boundary conditions
In this paper, we study the existence of positive solutions for the singular second order integral boundary value problem {u ''(t) + a(t) u'(t) + b(t) u(t) + c(t)f(u) = 0, t is an element of (0, 1), u(0) = integral(1)(0) g(s)u(s)ds, u(1) = integral(1)(0) h(s)u(s)ds, where c(t) is allowed to be singular at t = 0, 1 and f (u) may be singular at u = 0. The existence of positive solutions for the above problem is established by applying the fixed point index theorems under some weaker conditions concerning the first eigenvalue corresponding to the relevant linear operator. The results obtained herein generalize and improve some known results including singular and non-singular cases. (C) 2012 Elsevier Ltd. All rights reserved.
positive solution singular integral boundary value problem fixed point index cone