On a class of damped vibration problems with obstacles

The main purpose of this paper is to study the following damped vibration problem equation(1.1)−ẍ=g(t)ẋ+f(t,x) satisfying equation(1.2)x(0)−x(2π)=ẋ(0)−ẋ(2π)=0,x(t)≥0,∀t∈Requation(1.3)ẋ(t0−)=−ẋ(t0+),ifx(t0)=0. The variational principles are given and some existence and multiplicity results of nonzero periodic solutions satisfying ,  and  are obtained.