On variational methods for a class of damped vibration problems
2007; Elsevier BV; Volume: 68; Issue: 6 Linguagem: Inglês
10.1016/j.na.2006.12.043
ISSN1873-5215
AutoresXian Wu, Shaoxiong Chen, Kaimin Teng,
Tópico(s)Nonlinear Differential Equations Analysis
ResumoIn the present paper, the following damped vibration problems: (1.1){ü(t)+q(t)u̇(t)=A(t)u(t)+∇F(t,u(t)),a.e. t∈[0,T]u(0)−u(T)=u̇(0)−eQ(T)u̇(T)=0, and (1.1λ){ü(t)+q(t)u̇(t)=A(t)u(t)+λ∇F(t,u(t)),a.e. t∈[0,T]u(0)−u(T)=u̇(0)−eQ(T)u̇(T)=0, are studied, where T>0, λ>0, q∈L1(0,T;R), Q(t)=∫0tq(s)ds, A(t)=[aij(t)] is a symmetric N×N matrix-valued function defined in [0,T] with aij∈L∞([0,T]) for all i,j=1,2,…,N and there exists a positive constant θ such that A(t)ξ⋅ξ≥θ|ξ|2 for all ξ∈RN and a.e. t∈[0,T]. The variational principles are given, and an existence theorem and three multiplicity theorems of periodic solutions are obtained.
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