The Asymptotic Manifold of a Nonlinear System of Differential Equations
نویسندگان
چکیده
provided ƒ(2, x) is "sufficiently small." Our results, which are another contribution to this area, are motivated by two recent studies. Brauer and Wong [ l ] have obtained quite general results on the asymptotic relationships between the solutions of (1) and (2). We significantly weaken the hypotheses of one of their results; see Theorem 1 below. Toroshelidze [4] considered the problem of perturbing the asymptotic manifold (see definitions below) of a nonlinear scalar equation. This concept is discussed formally and in a more general setting by using systems (1) and (2); some related problems are also considered. The techniques used in the proofs are a combination of the wellknown comparison principle and the Schauder-Tychonoff fixed point theorem. Fundamental in the application of the comparison principle is a scalar equation
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