On the existence and nonexistence of periodic solutions to some nonlinear hyperbolic equations
The author considers multidimensional hyperbolic equations with nonlinear principal part. For a class of nonlinear hyperbolic equations with homogeneous terms the method of separation of variables and variational approach is used to prove the existence of periodic solutions. The proof of the nonexistence of nontrivial periodic solutions is based on new hyperbolic variational identities. The results are represented without proofs which will be published elsewhere.
scientific article; zbMATH DE number 1557540