A monotonicity method for solving hyperbolic problems with hysteresis
Pavel Krejčı́ · Applications of Mathematics · 1988
A version of the Minty-Browder method is used for proving the existence and uniqueness of a weak $\omega$-periodic solution to the equation $u_{tt}\rightarrow \text {div} F(\text {grad } u)= g$ in a bounded domain $\Omega \subset \bold R^N$ with the boundary condition $u=0$ on $\delta \Omega$, where $g$ is a given (generalized) $\omega$-periodic function and $F$ is the Ishlinskii hysteresis operator.