Necessary and sufficient conditions for existence and uniqueness of bounded and almost-periodic solutions of nonlinear differential equations

Nonlinear ordinary differential equations and systems (34A34) General theory of ordinary differential operators (47E05) Growth and boundedness of solutions to ordinary differential equations (34C11) Applications of operator theory to differential and integral equations (47N20) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27)

Related Items (9)

To Favard's theory for functional equations ⋮ Invertibility conditions for nonlinear autonomous differential operators in the space of functions bounded on the axis ⋮ Almost periodic solutions of differential equations ⋮ Conditions for the existence of solutions of difference equations in the metric space of bounded sequences ⋮ Necessary and sufficient conditions for the invertibility of nonlinear differentiable maps ⋮ Conditions of solvability for nonlinear differential equations with perturbations of the solutions in the space of functions bounded on the axis ⋮ Slowly oscillating solutions for differential equations with strictly monotone operator ⋮ On the Favard theory without \(\mathcal{H}\)-classes for differential-functional equations in Banach spaces ⋮ Necessary and sufficient conditions for the existence and \(\varepsilon \)-uniqueness of bounded solutions of the equation \(x^{\prime} = f(x) - h(t)\)

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