Two-sided Remotely Almost Periodic Solutions of Ordinary Differential Equations in Banach Spaces

The aim of this paper is studying the two-sided remotely almost periodic solutions of ordinary differential equations in Banach spaces of the form $x^{\mathrm{\prime }}=A(t)x+f(t)+F(t,x)$ with two-sided remotely almost periodic coefficients if the linear equation $x^{\mathrm{\prime }}=A(t)x$ satisfies the condition of exponential trichotomy and nonlinearity $F$ is “small”.