Boundary value problems on the half-line for a generalised Painlevé II equation
type: Item
instance of: scholarly article
title: Boundary value problems on the half-line for a generalised Painlevé II equation
zbMATH Open document ID: 1177.34042
author: Pablo Amster
author: Leonardo Vicchi
author: Colin Rogers
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-06-09T00:00:00Z
review text: Consider the differential equations \[ p''=a|p|^\gamma p+b |p|^\delta pp'\pm xp+c \tag{\((1)^\pm\)} \] with constants \(a>0\), \(\gamma\geq 0\), \(\delta\geq 0\), \(b\in\mathbb{R}\) \(c\in \mathbb{R}_*\) for \(0\leq x<\infty\). The authors prove the existence of at least one solution of \((1)^+\) satisfying the boundary conditions \[ p(0)=p_0,\;\lim_{x\to+ \infty}p(x)=0, \] and at least one solution of \((1)^-\) satisfying \[ p(0)=p_0,\;\lim_{x\to+ \infty}\frac{p(x)}{x}=0 \] in case \(\gamma>\max\{1,\delta\}\). The proofs are based on lower and upper solutions technique.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34B40
zbMATH DE Number: 5563018
MaRDI profile type: Publication
full work available at URL: j.na.2008.10.036
OpenAlex ID: W2006986176
cites work: A boundary value problem associated with the second Painleve transcendent and the Korteweg-de Vries equation
cites work: ON A PAINLEVÉ-TYPE BOUNDARY-VALUE PROBLEM
cites work: On a family of solutions of the second Painlevé equation related to superconductivity
cites work: Painlevé structure of a multi-ion electrodiffusion system
cites work: On a Painlevé II model in steady electrolysis: Application of a Bäcklund transformation
cites work: Dirichlet and periodic-type boundary value problems for Painlevé II
cites work: Q5703730
cites work: On two-point boundary value problems in multi-ion electrodiffusion.
cites work: On boundary value problems in three-ion electrodiffusion
DOI: 10.1016/J.NA.2008.10.036
description: scientific article; zbMATH DE number 5563018