ASYMPTOTIC BEHAVIOUR OF SOLUTIONS TO CERTAIN PROBLEMS INVOLVING NON-LINEAR DIFFERENTIAL EQUATIONS CONTAINING A SMALL PARAMETER MULTIPLYING THE HIGHEST DERIVATIVES

Abstract

CONTENTS Introduction Chapter I. Asymptotically stable case. Asymptotic behaviour of the solution to the initial-value problem § 1. Passage to the limit in the Cauchy problem § 2. Construction of the asymptotic expansion Chapter II. Asymptotically stable case. Problems that can be investigated on the basis of the asymptotic behaviour found for the Cauchy problem § 1. Two-point boundary-value problem. The solution for which, in the limit, z has a discontinuity at one end of the interval § 2. Two-point boundary-value problem. The solution for which, in the limit, z has a discontinuity at an interior point of the interval § 3. Problems with other supplementary conditions § 4. The solution for which, in the limit, y has a discontinuity at one end of the interval Chapter III. Hyperbolic case § 1. Periodic solutions § 2. Two-point boundary-value problem. The solution for which, in the limit, z has a discontinuity at the ends of the interval § 3. Two-point boundary-value problem. The solution for which, in the limit, z has a discontinuity at several interior points of the interval References