Stable time periodic solutions for damped sine-Gordon equations. (English) Zbl 1115.35118
Summary: We investigate existence and stability of time periodic solutions for damped sine-Gordon equations with delay under reasonable assumptions. The key-step is constructing suitable Lyapunov functionals and establishing an a priori bound for all possible periodic solutions. We also use the Schaefer fixed-point theorem.
MSC:
35Q53 | KdV equations (Korteweg-de Vries equations) |
35R10 | Partial functional-differential equations |
35B35 | Stability in context of PDEs |
35B10 | Periodic solutions to PDEs |