On the existence of solutions of a class of singular nonlinear two-point boundary value problems

Abstract

We examine the existence of solutions of the class of singular nonlinear two-point boundary value problems: −(y″ + (α/x)/y′) = ƒ(x, y), 0 < x < 1, y'(0 +) = 0 , y(1) = A, for α ⩾ 1. We show that for every a ⩾ 1, a unique solution of the singular two-point boundary value problem exists provided u ∗ < k 1 , where u ∗ = sup ϖƒ/ϖy and and k 1 is the first positive zero of J ( α − 1)/2 (√ k) ( J v ( z) is Bessel's function of the first kind of order v). Interestingly, k 1 is a monotonically increasing function of α; values of k 1 for some values of α are tabulated.