A Liouville property for Schrödinger operators
✍ Scribed by Alexander Grigor'yan; Wolfhard Hansen
- Publisher
- Springer
- Year
- 1998
- Tongue
- English
- Weight
- 534 KB
- Volume
- 312
- Category
- Article
- ISSN
- 0025-5831
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📜 SIMILAR VOLUMES
In this paper, we derive a Liouville type theorem on a complete Riemannian manifold without boundary and with nonnegative Ricci curvature for the equation \(\Delta u(x)+h(x) u(x)=0\), where the conditions \(\lim _{r \rightarrow x} r^{-1} \cdot \sup _{x \in B_{p}(r)}|\nabla h(x)|=0\) and \(h \geqslan
We prove multidimensional analogs of the trace formula obtained previously for one-dimensional Schro dinger operators. For example, let V be a continuous function on [0, 1] & /R & . For A/[1, ..., &], let &2 A be the Laplace operator on [0, 1] & with mixed Dirichlet Neumann boundary conditions .(x)=