Dirichlet problem for semilinear hyperbolic equation. Multidimensional case

the solvability of the Dirichlet problem for the semilinear equation of the vibrating string xtt (t, y) − x(t, y) + f (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. © 2007 Elsevier Inc. All rights reserved.