Asymptotic expansion of oscillatory bifurcation curves of ODEs with nonlinear diffusion.
type: Item
instance of: scholarly article
title: Asymptotic expansion of oscillatory bifurcation curves of ODEs with nonlinear diffusion.
zbMATH Open document ID: 1463.34157
author: Tetsutaro Shibata
published in: Differential and Integral Equations
publication date: 2020-07-02T00:00:00Z
review text: This work studies positive solutions of two-point boundary value problems of the form \[[u^p\cdot u']'+\lambda[u^1+\sin(u^n)],\quad u(0)=u(1)=0.\] The aim is to understand the curve of solutions in dependence on the parameter \(\lambda\). This is done by considering the norm \(\alpha=\|u\|_\infty\), and looking at the dependence of \(\lambda\) on \(\alpha\). An asymptotic formula for \(\lambda(\alpha)\) is proved, in particular showing the oscillatory behavior of this function as \(\alpha\rightarrow\infty\).
reviewed by: Guy Katriel
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34B09
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 7217173
zbMATH Keywords: boundary value problem
zbMATH Keywords: nonlinear eigenvalue problem
zbMATH Keywords: bifurcation
zbMATH Keywords: asymptotic expansion
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 7217173