### A direct proof of a theorem by Kolmogorov in hamiltonian systems

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This paper is chiefly a survey of results obtained in recent years on the asymptotic behaviour of semigroups of bounded linear operators on a Banach space. From our general point of view, discrete families of operators ${T}^{n}:n=0,1,...$ on a Banach space X (discrete one-parameter semigroups), one-parameter ${C}_{0}$-semigroups $T\left(t\right):t\ge 0$ on X (strongly continuous one-parameter semigroups), are particular cases of representations of topological abelian semigroups. Namely, given a topological abelian semigroup S, a family of bounded...

In this paper, using Mawhin's continuation theorem of the coincidence degree theory, we obtain some sufficient conditions for the existence of positive almost periodic solutions for a class of delay discrete models with Allee-effect.