Solutions of a nonlinear boundary value problem with a large parameter
type: Item
instance of: scholarly article
title: Solutions of a nonlinear boundary value problem with a large parameter
zbMATH Open document ID: 0944.34011
author: W. Fang
author: H. Gingold
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-09-22T00:00:00Z
review text: The ordinary differential equation \[ u_{xx}+ u^p= 0,\quad x\in (-L, L), \] is considered together with the Dirichlet boundary conditions \(u(-L)= u_\ell\), \(u(L)= u_r\). Depending on \(p\), \(u_\ell\), \(u_r\), the existence or nonexistence, the number and structure of solutions are studied. Their limits as \(p\to\infty\) are described, which are piecewise linear functions.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 1340186
zbMATH Keywords: nonlinear Dirichlet problem
zbMATH Keywords: structure of solutions
zbMATH Keywords: large parameter
zbMATH Keywords: limits of solutions
reviewed by: Sergei A. Brykalov
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6463
OpenAlex ID: W2037667211
cites work: Q5710735
cites work: Flattening of ellipses by growing nonlinearities
cites work: On the Existence of Positive Solutions of Semilinear Elliptic Equations
cites work: Q5516356
cites work: On the Generalized Emden–Fowler Equation
DOI: 10.1006/JMAA.1999.6463
description: scientific article; zbMATH DE number 1340186