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

Research output: Contribution to journalArticlepeer-review

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 (Formula presented.), as (Formula presented.), for a nonzero vector ξ and an explicit number p>0.

Original languageEnglish
Pages (from-to)79-107
Number of pages29
JournalDynamical Systems
Volume39
Issue number1
DOIs
StatePublished - 2024

Keywords

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

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