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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