摘要：We study positive solutions to steady-state reaction–diffusion models of the form $$ \textstyle\begin{cases} -\Delta u=\lambda f(v);\quad\Omega, \\ -\Delta v=\lambda g(u);\quad\Omega, \\ \frac{\partial u}{\partial \eta } \sqrt{\lambda } u=0;\quad \partial \Omega, \\ \frac{\partial v}{\partial \eta } \sqrt{\lambda }v=0; \quad\partial \Omega, \end{cases} $$ where $\lambda >0$ is a positive parameter, Ω is a bounded domain in $\mathbb{R}^{N}$ $(N > 1)$ with smooth boundary ∂Ω, or $\Omega =(0,1)$ , $\frac{\partial z}{\partial \eta }$ is the outward normal derivative of z. We assume that f and g are continuous increasing functions such that $f(0) = 0 = g(0)$ and $\lim_{s \rightarrow \infty } \frac{f(Mg(s))}{s} = 0$ for all $M>0$ . In particular, we extend the results for the single equation case discussed in (Fonseka et al. in J. Math. Anal. Appl. 476(2):480-494, 2019) to the above system.
