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Quasi-Solutions and Their Role in the Qualitative Theory of Differential Equations

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Quasi-Solutions and Their Role in the Qualitative Theory of Differential Equations

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Title: Quasi-Solutions and Their Role in the Qualitative Theory of Differential Equations
Author: Lakshmikantham, V.; Deimling, K.
Abstract: In the study of comparison theorems and extremal solutions for systems of ordinary differential equations [5], one usually imposes a condition on the right hand side known as quasi-monotone nondecreasing property. This property. is also needed in proving comparison theorems for second order, boundary value problems [9] as well as for the initial boundary value problem for parabolic systems [5, 6]. Also, it is well known that in the .method of vector Lyapunov functions which provides an effective tool to investigate the stability of Large Scale Systems [1-4], an unpleasant drawback is the requirement of the quasi-monotone property for the comparison systems. In systems which represent physical situations, we rather often find that this property is not satisfied.
URI: http://hdl.handle.net/10106/2204
Date: 1979-08

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