Stability and traveling waves of diffusive predator-prey model with age-structure and nonlocal effect

The paper is concerned with the dynamical behaviors of a stage-structured diffusive predator-prey model with nonlocal effect and harvesting. The linear stability of the equilibria is investigated by using the characteristic equation technique. By constructing a closed convex set bounded by a pair of upper-lower solutions and using Schauder fixed point theorem, the existence of traveling wave solution connecting two steady states is also derived. Finally, a pair of upper-lower solutions is constructed by using inequality technique and characteristic equations.