### A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

This paper is devoted to the spectral analysis of a non elliptic operator $A$, deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator $A$ has been derived, we determine its continuous spectrum. Then, we show that $A$ is unbounded from below and that it has a sequence of negative eigenvalues tending to $-\infty $. Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some conditions...