Asymptotic representations of solutions of essentially nonlinear systems of ordinary differential equations with regularly and rapidly varying nonlinearities

Abstract

1. Statement of the Problem and Auxiliary Notation Consider a system of differential equations y 0 i D ipi.t/’iC1.yiC1/; iD1;n; (1.1) in which 2 i 2 f1;1 g; i D 1;n; and piWaa;!a ! c0;C1a; i D 1;n; are continuous functions, 1 < a < ! C1; 3 and ’iWA.Y 0 i /!c0IC1a; i D 1;n; where A.Y 0