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Eigenvalues for a class of homogeneous cone maps arising from max-plus operators
1. | Division of Applied Mathematics, Brown University, Providence, RI 02912, United States |
2. | Department of Mathematics, Rutgers University, Piscataway, NJ 08854, United States |
$\max_{t\in J(s)} a(s, t)x(t) = \lambda x(s)$
arising from so-called "max-plus operators," where we seek a nonnegative eigenfunction $ x\in C[0, \mu]$ and eigenvalue $\lambda$. Here $J(s) = [\alpha(s), \beta(s)] \subset [0, \mu]$ for $s\in [0, \mu]$, with $a, \alpha$, and $\beta$ given functions, and the function $a$ nonnegative.
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