A basis theorem for a class of max-plus eigenproblems.
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 \(c\).
scientific article; zbMATH DE number 1915528