Existence and iteration of n symmetric positive solutions for a singular two-point boundary value problem

Abstract

Let n be an arbitrary natural number. In this paper, we consider the existence of n symmetric positive solutions and establish a corresponding iterative scheme for the two-point boundary value problem w″(t)+h(t)f(w(t)) = 0, 0 < t < 1, αw(0) − βw′(0) = 0, α(1) + βw′(1) = 0 The main tool is the monotone iterative technique. Here, the coefficient h( t) is symmetric on (0, 1) and may be singular at both end points t = 0 and t = 1.