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The aim of this paper is to extend the classical linear condition concerning diagonal dominant bloc matrix to fully nonlinear equations. Even if assumptions are strong, we obtain an explicit condition which exactly extend the one known in linear case, and the setting allows also to consider bicontinuous operator instead of the schift and as particular case, we receive periodic or almost periodic solutions for discrete time equations.

In this paper, we are concerned with periodic, quasi-periodic (q.p.) and almost periodic (a.p.) Optimal Control problems. After defining these problems and setting them in an abstract setting by using Abstract Harmonic Analysis, we give some structure results of the set of solutions, and study the relations between periodic and a.p. problems. We prove for instance that for an autonomous concave problem, the a.p. problem has a solution if and only if all problems (periodic with fixed or variable...

In this paper, we are concerned with periodic, quasi-periodic (q.p.) and almost periodic (a.p.) Optimal Control problems. After defining these problems and setting them in an abstract setting by using Abstract Harmonic Analysis, we give some structure results of the set of solutions, and study the relations between periodic and a.p. problems. We prove for instance that for an autonomous concave problem, the a.p. problem has a solution if and only if all problems (periodic with fixed or variable...

In this paper we prove the existence and uniqueness of $C^{\left(n\right)}$-almost periodic solutions to the nonautonomous ordinary differential equation $x^{\text{'}}\left(t\right)=A\left(t\right)x\left(t\right)+f\left(t\right)$, $t\in ℝ$, where $A\left(t\right)$ generates an exponentially stable family of operators $\left(U\right(t,s\left)\right)$ $t\ge s$ and $f$ is a $C^{\left(n\right)}$-almost periodic function with values in a Banach space $X$. We also study a Volterra-like equation with a $C^{\left(n\right)}$-almost periodic solution.