Existence of additional unstable equilibria for some monostable systems

We prove the existence of additional unstable equilibria E±E± for a class of “monostable” reaction–diffusion systems ut=Auxx+f(u),u(x,t)∈RN, having known equilibria SSE±>S yields two one-parameter families of travelling waves connecting SS to E±E± in addition to the family connecting SS to TT.