Triple positive solutions of conjugate boundary value problems
type: Item
instance of: scholarly article
title: Triple positive solutions of conjugate boundary value problems
zbMATH Open document ID: 0936.34018
DOI: 10.1016/S0898-1221(98)00190-4
publication date: 2000-05-08T00:00:00Z
review text: The author considers the following continuous boundary value problem: \[ \begin{gathered} (-1)^{n-p}y^{(n)}=a(t)h(y), \quad n\geq 2, \;t\in (0,1),\tag{1}\\ y^{(i)}(0)=0, \quad 0\leq i \leq p-1,\qquad y^{(i)}(1)=0, \quad 0\leq i \leq n-p-1, \end{gathered} \] and the discrete one: \[ \begin{gathered} (-1)^{n-p}\Delta^n y= F(k,y,\Delta y, \dots, \Delta^{n-1}y) , \quad n\geq 2, \;0\leq k\leq m, \tag{2}\\ \Delta^i y(0)=0, \quad 0\leq i \leq p-1, \qquad \Delta^i y(m+p+1)=0, \quad 0\leq i \leq n-p-1,\end{gathered} \] where \(1\leq p\leq n-1\) is fixed, \(h\) is a positive and nondecreasing function, \(a(t)\) is positive. Criteria are given for the existence of at least three positive solutions to boundary value problems (1) and (2). The criteria provide estimates on the norms of these positive solutions. As an application, the existence of radial solutions to certain partial difference equations is proved. The main tools of this study are fixed point theorems for operators on a cone.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 39A70
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 47B39
zbMATH DE Number: 1371503
zbMATH Keywords: conjugate boundary value problem
zbMATH Keywords: positive solutions
zbMATH Keywords: triple solutions
zbMATH Keywords: radial solution
zbMATH Keywords: difference equation
zbMATH Keywords: differential equation
author: Patricia J. Y. Wong
reviewed by: S. Yanchuk
MaRDI profile type: Publication
cites work: Q3732891
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full work available at URL: s0898-1221(98)00190-4
OpenAlex ID: W4213174683
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 1371503