Nonlinear wave equation

Nonlinear wave equation

A general nonlinear wave equation can be expressed as

where $f(x,t,s)$ is a continuous, monotonic increasing or decreasing (in $s$)real function on $[0,\pi ]\times {ℝ}^2$ and $2\pi$-periodic in $t$.Nontrivial periodic solutions are of interest in many applications. Existence ofmultiple or even infinitely many periodic solutions to some special casesof (NWE), e.g., $f(x,t,s)$ is superlinear in $s$ and/or independent of the time$t$, have been proved by many authors such as P. Rabinowitz, V. Benci, M. Berti, etc.