Existence of solutions for a nonlinear wave equation - Galewski, Marek; Nowakowski, Andrzej (Topological Methods in Nonlinear Analysis, 2006)
We prove the existence of a strong solution of a periodic-Dirichlet problemfor the semilinear wave equation with irrational period and withnonlinearity satisfying some general growth conditions locally around $0$.We construct a new variational method, called a dual method, and usingrelations between critical points and critical values of the primal actionand the dual action functionals we prove that the solution exists. The dualfunctional which we define is different from the ones known so far in thatit depends on two dual variables.