The qualitative analysis of a dynamical system of differential equations arising from the study of multilayer scales on pure metals II
Robert J. Baker · Proceedings of the American Mathematical Society · 1999
We provide a qualitative analysis of the n n -dimensional dynamical system: \[ q ˙ i = − ∑ j = 1 n a i j q j k , q i ( t ) > 0 , i = 1 , … , n , \dot q_i=-\sum _{j=1}^n \frac {a_{ij}}{q_j^k},\quad q_i(t)>0,\qquad i=1,\dots , n, \] where k k is an arbitrary positive integer. Under mild algebraic conditions on the constant matrix A = ( a i j ) A=(a_{ij}) , we show that every solution q ( t ) \mathbf q(t) , t ∈ [ 0 , a ) t\in [0,a) , extends to a solution on [ 0 , + ∞ ) [0,+\infty ) , such that lim t →