In this paper, we consider a two-species Lotka-Volterra competition model in one-dimensional spatially inhomogeneous environments. It is assumed that two competitors have the same movement strategy but slightly differing in their inter- and intra-specific competition rates. By using the Lyapunov-Schmidt reduction technique as well as some analytic skills, we find that the existence and stability of coexistence states can be determined by some scalar functions, and hence the unique coexistence state of the system is established in certain cases.
"Existence and Stability of Coexistence States for a Reaction-diffusion-advection Model." Taiwanese J. Math. 21 (4) 865 - 880, 2017. https://doi.org/10.11650/tjm/7514