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2011, Volume 2011: 931-940. Doi: 10.3934/proc.2011.2011.931 open access
This issue Previous Article Positive solutions for p-Laplacian equations with concave terms Next Article Convergence versus periodicity in a single-loop positive-feedback system 2. Periodic solutions

Convergence versus periodicity in a single-loop positive-feedback system 1. Convergence to equilibrium

  • 1.

    Dipartimento di Matematica, Università di Bari, via Orabona 4, 70125 Bari

  • 2.

    Department of Mathematics and Statistics, Parker Hall, Auburn University, AL 36849-5310

Received:  July 31, 2010
Revised:  March 31, 2011
Published:  August 2017
Abstract Related Papers Cited by
    Abstract
  • We study a parameter-dependent single-loop positive-feedback system in the nonnegative orthant of $\mathbb{R}^n$, with $n\in\mathbb{N}$, that arises in the analysis of the blow-up behavior of large radial solutions of polyharmonic PDEs with power nonlinearities. We describe the global dynamics of the system for arbitrary $n$ and prove that, in every dimension $n\<=4$, all forward-bounded solutions converge to one of two equilibria (one stable, the other unstable). In Part 2 of the paper, we will establish the existence of nontrivial periodic orbits in every dimension $n \>= 12$.
    Mathematics Subject Classification: Primary: 34C12; Secondary: 34C23; 34C25, 35B44.

    Citation:
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