NONLOCAL DIFFUSION ELLIPTIC SYSTEM MODELLING THE BEHAVIOUR OF A BACTERIA AND A LIVING NUTRIENT - Costa, Marcos Antonio Viana [UNESP]; Carranza, Yino Cueva [UNESP]; Morales-Rodrigo, Cristian; Suárez, Antonio (American Institute of Mathematical Sciences (AIMS), 2025)
In this paper, we discuss the existence and uniqueness of coexistence states for a class of non-local elliptic system. This problem models the behaviour of a bacteria and a living nutrient, whose diffusion depends on the population of the bacteria in a non-local and nonlinear way. Mainly, we employ bifurcation methods and the Implicit Function Theorem to obtain the existence and uniqueness of positive solution.
Keywords: coexistence states; global bifurcation; local bifurcation; Nonlocal coefficient diffusion; uniqueness of positive solution