Oscillations of a forced asymmetric oscillator at resonance

We consider the equation

where x⁺= max{x , 0}; x ¯ = max{-x , 0}, in a situation of resonance for the period 2 , i.e. when 1/(µ)^1/2+ 1/( )^1/2= 2/nfor some integer n . We assume that eis 2 -periodic, that fhas limits f(± ) at ± , and that the function ghas a sublinear primitive. Denoting by a solution of the homogeneous equation , we show that the behaviour of the solutions of the full nonlinear equation depends crucially on whether the function

is of constant sign or not. In particular, existence results for 2 -periodic and for subharmonic solutions, based on the function , are given.