Positive solutions for a class of boundary value problems on infinite intervals
type: Item
instance of: scholarly article
title: Positive solutions for a class of boundary value problems on infinite intervals
zbMATH Open document ID: 0823.34027
DOI: 10.1007/BF01197747
author: Donal O'Regan
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 1995-10-30T00:00:00Z
review text: Results concerning the existence of nonnegative solutions of the boundary value problem \({1 \over p(t)} (p(t)y')' = q(t)f(t,y,p(t)y')\), \(0 < t < \infty\), \(\lim_{t \to 0+} p(t)y'(t) = 0\) on \[ -\alpha y(0) + \beta \lim_{t \to 0+} p(t)y'(t) = 0,\;\alpha > 0,\;\beta > 0,\;\lim_{t \to \infty} y(t) = 0, \] are established by employing usual techniques. Examples are given to illustrate the results. The motivation for the present work has come from the works of \textit{F. V. Atkinson} and \textit{L. A. Peletier} [Arch. Ration. Mech. Anal. 93, 103-127 (1986; Zbl 0606.35029)] and \textit{K. Mcleod} and \textit{J. Serrin} [Arch. Ration. Mech. Anal. 99, 115-145 (1987; Zbl 0667.35023)].
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 736836
zbMATH Keywords: nonnegative solutions
zbMATH Keywords: boundary value problem
MaRDI profile type: Publication
cites work: Ground states of \(-\Delta u=f(u)\) and the Emden-Fowler equation
cites work: Infinite interval boundary value problems for \(y'' = f(x,y)\)
cites work: Existence of solutions for nonlinear singular boundary value problems
cites work: Computational methods for generalized Thomas-Fermi models of neutral atoms
cites work: A continuation method on locally convex spaces and applications to ordinary differential equations on noncompact intervals
cites work: Boundary value problems on infinite intervals and semiconductor devices
cites work: Uniqueness of positive radial solutions of \(\Delta u+f(u)=0\) in \({\mathbb{R}}^ n\)
cites work: Some existence principles and some general results for singular nonlinear two point boundary value problems
cites work: On the solvability of singular BVPs for second-order ordinary differential equations
cites work: Boundary value problems for infinite systems of second order differential equations
description: scientific article; zbMATH DE number 736836