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MR1112067 (92m:34145) 34G20 (34C35 47H20 47N20 58F25 58F39)
Smith, Hal L.; Thieme, Horst R. Convergence for strongly order-preserving semiflows. SIAM J. Math. Anal. 22 (1991), no. 4, 1081–1101.
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