Existence of traveling wave solutions for a nonlocal bistable equation: an abstract approach

Abstract

We consider traveling fronts to the nonlocal bistable equation. We do not assume that the Borel-measure is absolutely continuous with respect to the Lebesgue measure. We show that there is a traveling wave solution with monotone profile. In order to prove this result, we would develop a recursive method for abstract monotone dynamical systems and apply it to the equation.