Existence theorems of periodic solutions for a class of damped vibration problems

摘要

In the present paper, we research the following damped vibration problem {u(t) + g(t)u(t) = del F(t,u(t)) a.e. t is an element of [0,T] u(0) - u(T) = u(0) - u(T) = 0, (1.1) where T > 0, g subset of L-infinity(0, T; R), G(t) = integral(t)(0) g(s)ds, G(T) = 0 and F: [0,T] x R-N > R. The variational principle is given, and three existence theorems for periodic solutions are obtained. (C) 2008 Elsevier Inc. All rights reserved.