Bifurcation of nodal solutions for the Moore-Nehari differential equation
type: Item
instance of: scholarly article
title: Bifurcation of nodal solutions for the Moore-Nehari differential equation
author: Ryuji Kajikiya
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2022-12-09T00:00:00Z
review text: This paper deals with the bifurcation of nodal solutions for the Moore-Nehari differential equation. If a solution of the equation is odd or even, it is said to be symmetric. For a non-negative integer \(n\), a solution is called an \(n\)-nodal solution if it has exactly \(n\) zeros in the given interval. If the solution is \(n\)-nodal and symmetric, it is called \(n\)-nodal symmetric. The author proves that the equation has a unique \(n\)-nodal symmetric solution \(u_{n}\left( x,\lambda\right).\) The author also shows that the curve \(\left( \lambda,u_{2n+1}\left(x,\lambda\right) \right) \) of odd solutions does not bifurcate, but the curve \(\left( \lambda,u_{2n}\left( x,\lambda\right) \right) \) of even solutions, which is an \(n\)-nodal asymmetric solution, bifurcates.
reviewed by: Fatma Hıra
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34B09
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 7630742
zbMATH Keywords: bifurcation
zbMATH Keywords: symmetric solution
zbMATH Keywords: nodal solution
MaRDI profile type: Publication
full work available at URL: s00030-022-00816-w
OpenAlex ID: W4308076978
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DOI: 10.1007/S00030-022-00816-W
description: scientific article; zbMATH DE number 7630742