Nonlinear extensions of the Perron-Frobenius theorem and the Krein-Rutman theorem

摘要

A unification version of the Perron-Frobenius theorem and the Krein-Rutman theorem for increasing, positively 1-homogeneous, compact mappings is given on ordered Banach spaces without monotonic norm. A Collatz-type minimax characterization of the positive eigenvalue with positive eigenvector is obtained. The power method in computing the largest eigenpair is also extended.