On a class of forced vibration problems with obstacles

The main purpose of this paper is to study the following damped vibration problems −¨x = q(x)|˙x|2 + g(t) ˙x +f (t) (1.1) with x(0)−x(2π)= ˙x(0)− ˙x(2π) = 0, x(t) 0, ∀t ∈ R (1.2) and ˙x t−0 =−˙x t+0 , if x(t0) = 0, (1.3) where ˙x t−0 = lim t→t0−0 ˙x(t), ˙x t+0 = lim t→t0+0 ˙x(t). The variational sets are given and some multiplicity results of periodic solutions satisfying (1.1)–(1.3) are obtained. © 2007 Elsevier Inc. All rights reserved