Entire solutions of a monostable age-structured population model in a 2D lattice strip

This paper is concerned with the entire solutions for a monostable age-structured population model in a 2D lattice strip, i.e., solutions defined in the whole space and for all time t∈Rt∈R. In the quasi-monotone case, we first establish the existence and asymptotic behavior of solutions of the equation without jj (∈Z∈Z) variable. Combining traveling wave fronts with different speeds and a solution without jj variable, the existence and qualitative features of entire solutions are then proved. In the non-quasi-monotone case, we introduce two auxiliary quasi-monotone equations and establish a comparison argument for the three systems. Some new entire solutions are then constructed by using the comparison argument, the traveling wave fronts and a solution without jj variable of the auxiliary equations.