Multiplicity of periodic solutions of nonlinear wave equations.
The goal of the present paper is to complete the description of the small amplitude periodic solutions of (1) \[ u_{tt}-u_{xx}+f(u)=0\quad u(t,0)=u(t,\pi)=0,\tag{1} \] where \(f(0)=f'(0)=0\). To this end the authors prove ``optimal'' multiplicity results, finding the minimal periods of the solutions and showing their regularity. Here the authors use the variational Lyapunov-Schmidt reduction and minimax arguments.
scientific article; zbMATH DE number 2062708