Pseudo almost periodic solutions for some differential equations in a Banach space

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Universite Cadi Ayyad, Marrakech, Morocco ^{[1
]}

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Nonlinear Anal Theory Methods Appl | / 7卷 / 1141-1155期

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Differential equations - Functions - Integral equations - Mathematical operators - Perturbation techniques - Theorem proving;

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摘要：

A pseudo almost periodic (PAP) function f(t) in a Banach space is a function that can be expressed as the sum of an almost periodic function g(t) and a continuous function e(t) which vanishes as t approaches infinity, and moreover is bounded and has a zero asymptotic mean value. The main theorem on PAP solutions of a pseudo almost periodic nonlinear perturbation of a linear autonomous ordinary differential equation is proven. The extension of the theorem to nonlinear equations is also discussed.

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