Schweizer, Ben2019-08-022019-08-022019-05-10http://hdl.handle.net/2003/38161http://dx.doi.org/10.17877/DE290R-20140The Helmholtz equation $ - \nabla \cdot (a \nabla u) - \omega^2 u = f$ is considered in an unbounded wave-guide $\Omega := \mathbb{R} \times S \subset \mathbb{R}^d$, where $S \subset \mathbb{R}^{d-1}$ is a bounded domain. The coefficient $a$ is strictly elliptic and (locally) periodic in the unbounded direction $x_1\in \mathbb{R}$. For non-singular frequencies $\omega$, we show the existence of a solution $u$. While previous proofs of such results were based on operator theory, our proof uses only energy methods.enHelmholtz equationwave-guideperiodic mediaFredholm alternative610Text