Multiplicity results for the wave system using the linking theorem

Abstract

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