Stability of Monostable Waves for a Nonlocal Equation with Delay and without Quasi-Monotonicity

By using the weighted-energy method combining continuation method, the exponential stability of monostable traveling waves for a delayed equation without quasimonotonicity is established, including even the slower waves whose speed are close to the critical speed. Particularly, the nonlinearity is nonlocal in the equation and the initial perturbation is uniformly bounded only at x = +∞ but may not be vanishing.