Solutions of minimal period for a semilinear wave equation
The paper is dedicated to existence of time-periodic solutions u(x,t) of the boundary value problem for a semilinear wave equation containing only the nonlinearity g(u). The solutions in question are of prescribed minimal period T. The main results are given in the form of the two basic existence theorems. The sufficient conditions of those include some restrictions on monotonicity, smoothness and growth of the function g(u). The proofs of the theorems use the generalized Morse index of a solution and the dual variational methods in a critical point theory. References, 22 in number, fully cover the stated problem.
scientific article; zbMATH DE number 4175568
scientific article