Singular nonlinear boundary value problems for second-order ordinary differential equations
type: Item
instance of: scholarly article
title: Singular nonlinear boundary value problems for second-order ordinary differential equations
zbMATH Open document ID: 0685.34017
DOI: 10.1016/0022-0396(89)90113-7
author: Paul Waltman
author: Juan A. Gatica
author: Vladimir I. Oliker
published in: Journal of Differential Equations
publication date: 1989-01-01T00:00:00Z
review text: The authors study the boundary value problem \((1)\quad y''+f(x,y)=0,\) \(\alpha y(0)-\beta y'(0)=0,\) \(\gamma y(1)+\delta y'(1)=0,\) where f: (0,1)\(\times (0,\infty)\to (0,\infty)\) is continuous and decreasing in y for each fixed x and integrable on [0,1] for each fixed y, \(\lim_{y\to 0^+}f(x,y)=\infty\) uniformly on compact subsets of (0,1). They establish an existence theorem for the problem (1) and state conditions under which the problem (1) has at most one positive solution. The technical arguments involve properties of solutions and the use of iterative techniques. A new fixed point theorem for cones, for decreasing mappings, is developed and used in proofs.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 4122357
zbMATH Keywords: iterative techniques
reviewed by: Jan Ohriska
MaRDI profile type: Publication
full work available at URL: 0022-0396(89)90113-7
OpenAlex ID: W1975221158
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description: scientific article; zbMATH DE number 4122357