The monotone iterative method and zeros of Bessel functions for nonlinear singular derivative dependent BVP in the presence of upper and lower solutions

✍ Scribed by Amit K. Verma

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 241 KB
• Volume: 74
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2011.04.037

✦ Synopsis

In this paper we consider a class of nonlinear singular boundary value problems

We assume that the source function f (x, y, x α y ′ ) is Lipschitz in x α y ′ and onesided Lipschitz in y. The initial approximations are an upper solution u 0 (x) and a lower solution v 0 (x) which can be ordered in one way, v 0 (x) ≤ u 0 (x), or the other, u 0 (x) ≤ v 0 (x). We propose an iterative scheme and establish the existence of solutions bounded by v 0 and u 0 , and allow ∂f /∂y to take both positive and negative values. The method is constructive in nature and can be used to generate solutions of the nonlinear singular boundary value problems.