Multiplicity results for the wave system using the linking theorem

Abstract

We investigate the existence of solutions of the one-dimensional wave system \begin{eqnarray*} & u_{tt} - u_{xx} + \mu g(u+v)= f(u+v) \qquad \mbox{ in } (- {\frac{\pi}{2}} , {\frac{\pi}{2}} ) \times R , \\ & v_{tt} - v_{xx} + \nu g(u+v)= f(u+v) \qquad \mbox{ in } (- {\frac{\pi}{2}} , {\frac{\pi}{2}} ) \times R , \end{eqnarray*} with Dirichlet boundary condition. We find them by applying linking inequlaities.