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We study positive solutions to the steady state reaction diffusion systems ofthe form: \begin{equation} \left\{\begin{array}{ll} -\Delta u = \lambdaf(v)+\mu h(u), & \Omega,\\ -\Delta v = \lambda g(u)+\mu q(v),& \Omega,\\\frac{\partial u}{\partial \eta}+\sqrt[]{\lambda +\mu}\, u=0,&\partial\Omega,\\ \frac{\partial v}{\partial \eta}+\sqrt[]{\lambda +\mu}\, v=0,& \partial\Omega,\\ \end{array}\right. \end{equation} where ${\lambda,\mu>0}$are positive parameters, ${\Omega}$ is a bounded in $\mathbb{R}^{N}$$(N>1)$with smooth boundary ${\partial \Omega}$, or ${\Omega=(0,1)}$, ${\frac{\partial z}{\partial \eta} }$ is the outward normal derivative of $z$.Here $f, g, h, q\in C^{2} [0,r)\cap C[0,\infty)$ for some $r>0$. Further, weassume that $f, g, h$ and $q$ are increasing functions such that $f(0) = g(0) =h(0) = {q}(0) = 0$, $f^\prime(0), g^\prime(0), h^\prime(0), q^\prime(0) > 0$,and $\lim\limits_{s\to \infty}\frac{f(M g(s))}{s}=0$ for all $M>0$. Undercertain additional assumptions on $f, g, h$ and $ q$ we prove our existence andmultiplicity results. Our existence and multiplicity results are proved usingsub-super solution methods.

On the existence and multiplicity of positive solutions to classes of steady state reaction diffusion systems with multiple parameters