Nonlinear singular BVP of limit circle type and the presence of reverse-ordered upper and lower solutions
type: Item
instance of: scholarly article
title: Nonlinear singular BVP of limit circle type and the presence of reverse-ordered upper and lower solutions
zbMATH Open document ID: 1239.34024
DOI: 10.1155/2011/986948
author: Lajja Verma
author: Amit K. Verma
published in: International Journal of Differential Equations
publication date: 2012-03-08T00:00:00Z
review text: Summary: We consider the following class of nonlinear singular differential equations \[ -(p(x)y'(x))' + q(x)f(x, y(x), p(x) y'(x)) = 0, ~0 < x < 1, \] subject to the Neumann boundary condition \[ y'(0) = y'(1) = 0. \] Conditions on \(p(x)\) and \(q(x)\) ensure that \(x = 0\) is a singular point of limit circle type. A simple approximation scheme which is iterative in nature is considered. The initial iterates are upper and lower solutions which can be ordered in one way \((v_0 \leq u_0)\) or the other \((u_0 \leq v_0)\).
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 6013239
zbMATH Keywords: approximation scheme
Wikidata QID: Q58686883
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/986948
OpenAlex ID: W2102648587
cites work: Positive Solutions of Singular Sublinear Dirichlet Boundary Value Problems
cites work: Existence, upper and lower solutions and quasilinearization for singular differential equations
cites work: The monotone iterative method and zeros of Bessel functions for nonlinear singular derivative dependent BVP in the presence of upper and lower solutions
cites work: A constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions
cites work: Two-point boundary value problems. Lower and upper solutions
cites work: Existence theory for nonresonant singular boundary value problems
cites work: Q3279399
description: scientific article; zbMATH DE number 6013239