Connecting orbits in scalar reaction diffusion equations. II: The complete solution (Q913113)

[For part I, see Dyn. Rep. 1, 57-89 (1988; Zbl 0679.35047).] In part I the authors studied the one-dimensional reaction-diffusion equation \[ u_ t=u_{xx}+f(u),\quad x\in (0,1) \] with Dirichlet boundary conditions \(u(t,0)=u(t,1)=0\), and obtained a partial answer to the question: (Q) Given a stationary (i.e. time-independent) solution of the above problem, which other stationary solutions does it connect to? The present paper answers completely this question by reducing the number of exclusion principles to two.