On the structure of the set of stationary solutions for a Lotka-Volterra competition model with diffusion (Q2731048)

This paper is devoted to the stationary solutions of a Lotka-Volterra competition model with diffusion NEWLINE\[NEWLINE\begin{cases} \vec u_t=\varepsilon \Delta\vec u_{xx}+\vec f(\vec u)\\ \vec u_x=0,\;x=0,1,\;t>0\end{cases}\tag{1}NEWLINE\]NEWLINE with suitable initial condition, where \(\vec u=(v,w)\), \(D=\text{diag} (1,d)\), \(\vec f(g,h)\), \(g(\vec u)=(1-v-cw)u\), \(h(\vec u)=(a-bv-w)w\), and every parameter is a positive constant. Here the author studies the structure of the set of stationary solutions for (1). The author uses both comparison principle and bifurcation theory.