Almost Periodic Solutions of Monotone Second-Order Differential Equations

作者：Ayachi Moez^*; Blot Joel; Cieutat Philippe

来源：Advanced Nonlinear Studies, 2011, 11(3): 541-554.

• Hilbert spaces
• Bohr-almost periodic
• Besicovitch-almost periodic
• maximal monotone operators

We give sufficient conditions for the existence of almost periodic solutions of the 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.

• 出版日期2011-8