Multiple solutions for an asymptotically linear wave equation

Abstract

We will be concerned with the multiplicity results for periodic solutions of the wave equation $(*)$ $u_{tt}-u_{xx}= f(x,t,u)$ satisfying some standard boundary and periodicity conditions. Our aim is to show that under some reasonable conditions on $f$ the above problem possesses at least three solutions in the non--equivariant case and to estimate the number of periodic solutions of $(*)$ when an action of $Z_2$ is involved.