In this paper we derive a lattice model with infinite distributed delay to describe the growth of a single-species population in a 2D patchy environment with infinite number of patches connected locally by diffusion and global interaction. We consider the existence of traveling wave solutions when the birth rate is large enough that each patch can sustain a positive equilibrium. When the birth ...

The propose of the paper is devoted to study existence ?-periodic solutions for second order delay differential equation in abstract Banach space. Firstly, we build a new maximum principle corresponding linear equation. Secondly, with help this principle, minimal and maximal periodic our concerns problem by means perturbation method monotone iterative technique lower upper solutions. In additio...

In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the generalized resolvent operator technique associated with the (A,η,m)-monotone operators, the approximation solvability of the operator equation problems and the convergence of iterativ...

This paper is concerned with the existence of extreme solutions of integral boundary value problems for a class of first order impulsive functional differential equations. We obtain the sufficient conditions for existence of extreme solutions by using upper and lower solutions method coupled with monotone iterative technique. An example is also discussed to illustrate the efficiency of the obta...