A Note on Nonautonomous Systems of Second-Order Differential Equations

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The main objective of this paper is twofold. We first revisit the concept of doubly weighted pseudo-almost automorphy and discuss some additional properties of these functions. Next, we make extensive use of dichotomy tools to study and obtain the existence of doubly weighted pseudo-almost automorphic solutions to some nonautonomous second-order systems of differential equations. As an illustration, we will consider a nonresonance case for some scalar second-order systems of second-order differential equations.