Solvability and stability of a semilinear wave equation with nonlinear boundary conditions

We discuss solvability for the semilinear equation of the vibrating string xtt(t,y)−Δx(t,y)+f(t,y,x(t,y))=0xtt(t,y)−Δx(t,y)+f(t,y,x(t,y))=0 in a bounded domain, and certain type of nonlinearity on the boundary. To this effect we derive a new dual variational method. Next we discuss stability of solutions with respect to initial conditions.