Long-time behaviour of solutions of superlinear systems of differential equations

ABSTRACT

This paper establishes the precise asymptotic behaviour, as time t tends to infinity, for nontrivial, decaying solutions of genuinely nonlinear systems of ordinary differential equations. The lowest order term in these systems, when the spatial variables are small, is not linear, but rather positively homogeneous of a degree greater than one. We prove that the solution behaves like $\xi t^{-p}$, as $t\to \mathrm{\infty }$, for a nonzero vector ξ and an explicit number p>0.

KEYWORDS:

• Superlinear differential equations
• nonlinear dynamical system
• long-time behaviour
• asymptotic approximation

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34D05
• 41A60

Disclosure statement

No potential conflict of interest was reported by the author(s).