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Zeitschrift für Analysis und ihre Anwendungen

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Volume 20, Issue 3, 2001, pp. 739–753
DOI: 10.4171/ZAA/1042

Published online: 2001-09-30

The Upper and Lower Functions Method for Second Order Systems

A. Ja. Lepin[1] and Felix Zh. Sadyrbaev[2]

(1) University of Latvia, Riga, Latvia
(2) University of Latvia, Riga, Latvia

Two-point boundary value problems for $m$-dimensional second order systems are considered. The method of upper and lower functions is applied to problems of the Dirichlet type and problems with nonlinear boundary conditions. The conditions on upper and lower functions are substantially relaxed comparing with the classical $C^2$-class and properties of them are studied for systems with monotone in $x$ right sides. Consequences for even order differential equations with mixed monotonicities are given.

Keywords: Monotone iterative techniques, upper and lower functions, maximal and minimal solutions, second order systems

Lepin A. Ja., Sadyrbaev Felix: The Upper and Lower Functions Method for Second Order Systems. Z. Anal. Anwend. 20 (2001), 739-753. doi: 10.4171/ZAA/1042