A basis theorem for a class of max-plus eigenproblems.
type: Item
instance of: scholarly article
title: A basis theorem for a class of max-plus eigenproblems.
zbMATH Open document ID: 1049.47055
DOI: 10.1016/S0022-0396(02)00087-6
author: John Mallet-Paret
author: Roger D. Nussbaum
published in: Journal of Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: The max-plus equation \(P+f(x) =\max \{ H(s) +f(c(s)) \mid x\leq s\leq M\}\), \(x\in [0,M]\), where \(H:[0,M] \to {\mathbb R}\) and \(c:[0,M] \to [0,M] \) are given functions, is considered in the present paper. The existence of a finite set (a basis) of eigensolutions with the same eigenvalue \(P\) is proved under general conditions on the functions \(f,\) \(H\) and \(c\).
reviewed by: Stepan Agop Tersian
Mathematics Subject Classification ID: 47J10
zbMATH DE Number: 1915528
zbMATH Keywords: max-plus operator
zbMATH Keywords: additive eigenvalue
MaRDI profile type: Publication
cites work: Q4304869
cites work: Linear Operators in Complete Positive Cones
cites work: An additive eigenvalue problem of physics related to linear programming
cites work: Minimax algebra
cites work: Q4782024
cites work: Q4438200
cites work: Risk-Sensitive Control of Finite State Machines on an Infinite Horizon I
cites work: Risk-Sensitive Control of Finite State Machines on an Infinite Horizon II
cites work: A Max-Plus-Based Algorithm for a Hamilton--Jacobi--Bellman Equation of Nonlinear Filtering
cites work: Q4337616
cites work: Eigenvalues for a class of homogeneous cone maps arising from max-plus operators
cites work: Boundary layer phenomena for differential-delay equations with state-dependent time lags: III.
cites work: Convergence of iterates of a nonlinear operator arising in statistical mechanics
cites work: Periodic points of positive linear operators and Perron-Frobenius operators
description: scientific article; zbMATH DE number 1915528