Communications in Contemporary Mathematics ( IF 1.278 ) Pub Date : 2020-06-22 , DOI: 10.1142/s0219199720500327 Julien Brasseur
In this paper, we study the asymptotic behavior as of solutions to the nonlocal stationary Fisher-KPP type equation where and . Under rather mild assumptions and using very little technology, we prove that there exists one and only one positive solution and that as where . This generalizes the previously known results and answers an open question raised by Berestycki et al. Our method of proof is also of independent interest as it shows how to reduce this nonlocal problem to a local one. The sharpness of our assumptions is also briefly discussed.