7 problems

Let $\Omega=B_R(0)\subset\mathbb{R}^2$ with $R>0$ and $k>0$. A steady state is a solution $(u,v)$ of the stationary problem considered in the paper, with prescribed mass…

Nondegeneracy conjecture. Given a network $G$, if

Consider the minimally bistable ERK subnetwork, and let a compatibility class be determined by the conserved quantities of the reaction system. Three-steady-state conjecture. For e…

Consider the full ERK network and the same network with $k_{\mathrm{on}}=0$, and let a positive steady state mean a steady state with all relevant concentrations positive; call a s…

Let $G$ be a reaction network consisting of one reversible-reaction pair $y\leftrightarrows y'$ and one irreversible reaction $\widetilde y\to\widetilde y'$. The reaction vectors a…

Let $G$ be a reaction network, and suppose that $G$ does not admit infinitely many positive steady states in any stoichiometric compatibility class. Recall that $G$ admits $k$ posi…

Nondegeneracy conjecture. Every network with finitely many positive steady states has the same capacity when capacity is counted using all positive steady states or only nondegener…