This paper is devoted to time-global solutions of the Fisher-KPP equation in ℝ N: where f is a
C 2 concave function on [0, 1] such that f (0)= f (1)= 0 and f> 0 on (0, 1). It is well known that …

In this paper, we establish several Liouville type theorems for entire solutions to fractional
parabolic equations. We first obtain the key ingredients needed in the proof of Liouville …

We study, on the entire space ℝN (N [ges] 1), the diffusive logistic equationand its
generalizations. Here p> 1 is a constant. Problem (1.1) plays an important role in …

This paper is concerned with entire solutions of the Fisher-KPP equation with nonlocal
dispersal, ie, ut= J∗ u− u+ f (u), which is a one-dimensional nonlocal version of the Fisher …

We study entire solutions of a scalar reaction-diffusion equation of 1-space dimension. Here
the entire solutions are meant by solutions defined for all $(x, t)\in\mathbb R^ 2$. Assuming …

We deal with a system of Lotka–Volterra competition-diffusion equations on R, which is a
competing two species model with diffusion. It is known that the equations allow traveling …

We consider traveling waves for a nonlinear diffusion equation with a bistable or multistable
nonlinearity. The goal is to study how a planar traveling front interacts with a compact …

We establish selection of critical pulled fronts in invasion processes as predicted by the
marginal stability conjecture. Our result shows convergence to a pulled front with a …

We consider the nonlocal analogue of the Fisher-KPP equation ut= μ∗ u− u+ f (u), where μ
is a Borel-measure on R with μ (R)= 1 and f satisfies f (0)= f (1)= 0 and f> 0 in (0, 1). We do …

This paper is concerned with entire solutions for bistable reaction-diffusion equations with
nonlocal delay in one-dimensional spatial domain. Here the entire solutions are defined in …