Dirichlet problem for semilinear hyperbolic equation

We discuss the solvability of the Dirichlet problem for the semilinear equation of the vibrating string xtt(t,y)-xyy(t,y)+f(t,y,x(t,y))=0 in rectangle with sides length being irrational numbers and superlinear nonlinearity. To this effect we derive new dual variational method.