Uniqueness of positive solutions of quasilinear differential equations
type: Item
instance of: scholarly article
title: Uniqueness of positive solutions of quasilinear differential equations
zbMATH Open document ID: 0831.34028
author: Yūki Naito
published in: Differential and Integral Equations
publication date: 1995-07-18T00:00:00Z
review text: The paper deals with differential equations of the form (1) \(|u' |m - 2u')' + p(t) f(u) = 0\), \(t \in (a,b)\), where \(m > 1\), \(p\) is continuous and positive on \((a,b)\), \(f\) is continuous on \(0, \infty)\), positive on \((0, \infty)\) and such that the function \({f(u) \over um - 1}\) is decreasing in \(u \in (0, \infty)\). In particular, the author proves uniqueness theorems for positive solutions of the equation (1) subjected to the boundary conditions \(u(a) = u'(b) = 0\), \(u'(a) = u(b) = 0\) and \(u(a) = u(b) = 0\), respectively. To this aim the notion of a generalized Prüfer transformation is introduced.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 775649
zbMATH Keywords: boundary value problem
zbMATH Keywords: quasilinear differential equation
zbMATH Keywords: uniqueness
zbMATH Keywords: generalized Prüfer transformation
reviewed by: Milan Tvrdý
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 775649