An infinite-dimensional extension of theorems of Hartman and Wintner on monotone positive solutions of ordinary differential equations

Author:
A. F. Izé

Journal:
Proc. Amer. Math. Soc. **110** (1990), 77-84

MSC:
Primary 34G20; Secondary 34C35, 58D25

MathSciNet review:
1015679

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Abstract: Consider the equation (1) , a Banach sequence space with a Schauder Basis. It is proved that if is a positive operator and the solution operator is compact for , then system (1) has at least one solution such that , and consequently are monotone nonincreasing for .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1015679-7

Keywords:
Differential equations,
Banach spaces,
infinite dimensional spaces,
positive solutions,
operator equations,
strongly positive,
solid cone,
egress points,
strict egress points,
trajectory,
orbit,
consequent operator,
left shadow,
process,
retract,
infinitesimal generator,
classical solution

Article copyright:
© Copyright 1990
American Mathematical Society