Global asymptotic behaviour in some functional parabolic equations (Q1612578)

The author considers a system of partial functional-differential equations with nonlocal spatio-temporal kernels. When the nonlinear terms satisfy certain nonmonotone properties (termed as quasimonotonicity and non-quasimonotonicity), it is shown that solutions to the system with non-zero initial data converge uniformly to a unique positive equilibrium. The method is via modification of the sub- and supersolution technique. The results extend some previous ones obtained for delay reaction-diffusion equations with nonlocal spatial effects.