(untitled) (Journal of Partial Differential Equations, 2020)
Consider the eigenvalue problem: &#916gu - &#955Ku = 0 in D where D is the unit disc of the complex plane, g is a complete metric conformal to the Poincar&#233 metric on D, and K is the Gaussian curvature. It is shown that if &#955 > 12 (&#955 > 14in the case of K &#8804 0), then the above problem has no positive solutions.