On the asymptotic growth of positive solutions to a nonlocal elliptic blow-up system involving strong competition

  • Susanna Terracini

    Dipartimento di Matematica “Giuseppe Peano”, Università di Torino, Via Carlo Alberto, 10, 10123 Torino, Italy
  • Stefano Vita

    Dipartimento di Matematica “Giuseppe Peano”, Università di Torino, Via Carlo Alberto, 10, 10123 Torino, Italy

Abstract

For a competition-diffusion system involving the fractional Laplacian of the form

with , we prove that the maximal asymptotic growth rate for its entire solutions is . Moreover, since we are able to construct symmetric solutions to the problem, when with prescribed growth arbitrarily close to the critical one, we can conclude that the asymptotic bound found is optimal. Finally, we prove existence of genuinely higher dimensional solutions, when . Such problems arise, for example, as blow-ups of fractional reaction-diffusion systems when the interspecific competition rate tends to infinity.

Cite this article

Susanna Terracini, Stefano Vita, On the asymptotic growth of positive solutions to a nonlocal elliptic blow-up system involving strong competition. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 3, pp. 831–858

DOI 10.1016/J.ANIHPC.2017.08.004