Bounded and almost automorphic solutions of some nonlinear differential equations in Banach spaces Original Research Article

We study some properties of bounded and almost automorphic solutions of the following nonlinear differential equation: x′=f(t,x),x′=f(t,x), Turn MathJax on where XX is a Banach space and f:R×X⟶Xf:R×X⟶X is almost automorphic with a parameter. We give sufficient conditions for the existence of almost automorphic solutions when the differential equation admits at least a solution with a relatively compact range defined on the half-line of positive numbers.