Abstract: We give sufficient conditions for the existence of almost periodic solutions of the following second-order differential equation: u′′(t) = f(u(t)) + e(t) on a Hilbert space H, where the vector field f : H −→ H is monotone, continuous and the forcing term e : R −→ H is almost periodic. Notably, we state a result of existence and uniqueness of the Besicovitch almost periodic solution, then we approximate this solution by a sequence of Bohr almost periodic solutions.
Abstract: By means of variational methods, we study the existence and uniqueness of almost periodic solutions for a class of second order neutral functional differential equations with infinite delay.
Abstract: To study the a.p. (almost periodic) solutions of retarded functional differential equations in the form $u''(t)=\int_{-r}^{0}D_{1}f(u(t),u(t+\theta))d\theta+\int_{-r}^{0}D_{2}f(u(t-\theta),u(t))d\theta $, we introduce variational formalisms to characterize the a.p. solutions as a critical points of functionals defined on Banach spaces of a.p. functions. We obtain an existence result of weak a.p. solutions and a result of density of the a.p. forcing termes e(.) for which the equation possesses usual a.p. solutions.
Abstract: We provide new variational settings to study the a.p. (almost periodic) solutions of a class of nonlinear neutral delay equations. We extend Shu and Xu (2006) variational setting for periodic solutions of nonlinear neutral delay equation to the almost periodic settings. We obtain results on the structure of the set of the a.p. solutions, results of existence of a.p. solutions, results of existence of a.p. solutions, and also a density result for the forced equations.
