@Article{JPDE-4-1, author = {Fang Hua Lin}, title = {An Eigenvalue Problem on Negatively Curved Manifolds}, journal = {Journal of Partial Differential Equations}, year = {1991}, volume = {4}, number = {4}, pages = {1--8}, abstract = { Consider the eigenvalue problem: Δgu - λKu = 0 \quad in D where D is the unit disc of the complex plane, g is a complete metric conformal to the Poincaré metric on D, and K is the Gaussian curvature. It is shown that if λ > \frac{1}{2} (λ > \frac{1}{4}in the case of K ≤ 0), then the above problem has no positive solutions.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5779.html} }