Almost periodic solutions of monotone second-order differential equations
M Ayachi, J Blot, P Cieutat - Advanced Nonlinear Studies, 2011 - degruyter.com
M Ayachi, J Blot, P Cieutat
Advanced Nonlinear Studies, 2011•degruyter.comWe give sufficient conditions for the existence of almost periodic solutions of the
secondorder 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.
secondorder 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
We give sufficient conditions for the existence of almost periodic solutions of the secondorder 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.
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