Existence and uniqueness of positive solutions for a singular second-order integral boundary value problem

Abstract

European Mathematical SocietyIn this work, we discuss the existence and uniqueness of positive solutions for the second order integral boundary value problem {xn(t) + f(t, x(t), (Hx)(t)) = 0, 0 < t < 1, x(0) = 0, x(1) = ∫01 a(s)x(s)ds, where the function f has a singularity at t0 = 0. Our main tool is a fixed point theorem of Wardowski (2012). Moreover, we present several examples illustrating our result.