On the effects of spatial heterogeneity on positive steady states of Lotka-Volterra competition model with advection

This paper is concerned with the steady-state problem of a Lotka-Volterra competition model with diffusion and advection, developed by Kuto and Tsujikawa (2015) [20] and Wang et al. (2015) [31]. When spatial heterogeneity is introduced into the model, we obtain some sufficient conditions for the existence and non-existence of positive steady states. Our results demonstrate the existence of a critical value for the parameter $b_1$ in this model such that below this critical value, spatial heterogeneity has little effect on the existence and non-existence of positive steady states, whereas significant changes occur once $b_1$ exceeds the critical value.