Geodesic
Stable time periodic solutions for damped sine-Gordon equations
Electronic journal of differential equations, Tome 2006 (2006)
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 the priori bound for all possible periodic solutions. We also use the Schaefer fixed-point theorem.
Classification : 34K13, 35K50
Keywords: Schaefer's fixed-point theorem, time periodic solutions, sine-Gordon equations, uniformly asymptotic stability 
@article{EJDE_2006__2006__a34,
     author = {Zhu,  Jianmin and Li,  Zhixiang and Liu,  Yicheng},
     title = {Stable time periodic solutions for damped {sine-Gordon} equations},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1115.35118},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a34/}
}
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Zhu,  Jianmin; Li,  Zhixiang; Liu,  Yicheng. Stable time periodic solutions for damped sine-Gordon equations. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a34/