Linking method applied to a class of a system of critical growth wave equations

We show the existence of at least two solutions for a class of a system of critical growth wave equations, with periodic condition on tt and the Dirichlet boundary condition utt−uxx=av+2αα+βu+α−1v+β+fin (−π2,π2)×R,vtt−vxx=bu+2βα+βu+αv+β−1+gin (−π2,π2)×R, where αα, β>1β>1 are real constants, u+=max{u,0}u+=max{u,0}. We first show that the system has a negative solution under suitable conditions on the matrix A=(0ab0), ff, gg, and next show that the system has another solution for the same conditions on AA, ff and gg by the linking arguments.