Traveling Waves for Monotone Semiflows with Weak Compactness

This paper is devoted to the study of traveling waves for monotone semiflows of monostable type with weak compactness. To weaken the compactness condition imposed in previous works, we construct a compact set in the kinetic phase space and use an abstract variant of Helly's theorem. The obtained result is then applied to three prototypical noncompact (even non-α-contractive) evolution systems.