A Poincaré determinant on the torus

Abstract

In this work we introduce a Poincaré determinant type for operators on the torus $\To^n$. As an application we establish the existence of nontrivial solutions for elliptic equations of the form $(-\Delta {)}^{\frac{\nu }{2}}u+Qu=0$ on $\To^n$ by using the Hill's method.

arXiv admin note: text overlap with arXiv:2012.13216