Uniqueness of Periodic Solutions for Asymptotically Linear Duffing Equations with Strong Forcing

so that we are dealing with an asymptotically linear problem. The forcing term p is T -periodic, and we are interested in T -periodic solutions of (1). We assume that the linear part of the equation is nonresonant, that is a 6= 0 and if c = 0 then a 6= (2πm/T ) for all integer m. Our result shows that for generic forcing term p, when the parameter λ, which measures the strength of the forcing, is sufficiently large, (1) has a unique T -periodic solution. The existence of a solution (for all λ) under the assumptions made above is a well-known application of degree theory or Schauder’s fixed point theorem (see [5] for existence results under much more general conditions), and it is the