Positive solutions to BVPs for a singular differential equation
type: Item
instance of: scholarly article
title: Positive solutions to BVPs for a singular differential equation
zbMATH Open document ID: 1130.34015
author: Xiaodan Wei
author: Wenshu Zhou
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-05-15T00:00:00Z
review text: The authors are concerned with existence of positive solutions for the singular second-order differential equation \[ \varphi''-\lambda\frac{| \varphi'| ^2}{\varphi}+f(t)=0,\quad t\in (0,1), \] subject to the boundary conditions \[ \varphi(1)=\varphi(0)=0\text{ or }\varphi'(1)=\varphi'(0)=0. \] In addition, the authors investigate uniqueness and asymptotic behavior of the solution as \(\lambda\to 0\) and as \(\lambda\to\infty\). The proof of the main results are based on the classical method of elliptic regularization. For related work, see [\textit{X. Zhang, L. Liu, Y. Wu}, Nonlinear Anal., Theory Methods Appl. 68, No.~1 (A), 97--108 (2008; Zbl 1135.34016)].
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B16
zbMATH DE Number: 5152816
zbMATH Keywords: Positive solution
zbMATH Keywords: Existence
zbMATH Keywords: Uniqueness
Wikidata QID: Q115343263
reviewed by: Ruyun Ma
MaRDI profile type: Publication
full work available at URL: j.na.2006.06.015
OpenAlex ID: W2056862939
cites work: Q4337944
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DOI: 10.1016/J.NA.2006.06.015
description: scientific article; zbMATH DE number 5152816