Wave equation in higher dimensions – periodic solutions

摘要

We discuss the solvability of the periodic-Dirichlet problem for the wave equation with forced vibrations xtt(t, y) ? ?x(t, y) + l(t, y, x(t, y)) = 0 in higher dimensions with sides length being irrational numbers and superlinear nonlinearity. To this effect we derive a new dual variational method.