SADDLE SOLUTIONS FOR A CLASS OF SYSTEMS OF PERIODIC AND REVERSIBLE SEMILINEAR ELLIPTIC EQUATIONS

We study systems of elliptic equations −∆u(x)+Fu(x, u) = 0 with potentials F ∈ C2(Rn,Rm) which are periodic and even in all their variables. We show that if F(x,u) has flip symmetry with respect to two of the compo- nents of x and if the minimal periodic solutions are not degenerate then the system has saddle type solutions on R