Unbounded solutions of the stationary Schrödinger equation on Riemannian manifolds

DOI10.1007/BF03321048zbMath1138.35306WikidataQ115390821 ScholiaQ115390821MaRDI QIDQ1884447

Victoriya Y. Chebanenko, Elena A. Mazepa, Alexander G. Losev

Publication date: 1 November 2004

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

zbMATH Keywords

Schrödinger equationunbounded solutionnon-compact Riemannian manifold

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15) Potentials and capacities, extremal length and related notions in higher dimensions (31B15) Classification theory of Riemann surfaces (30F20)

Related Items (max. 100)

On the solvability of boundary value problems for the inhomogeneous Schrödinger equation on model Riemannian manifolds ⋮ Boundary-value problems for the inhomogeneous Schr"odinger equation with variations of its potential on non-compact Riemannian manifolds ⋮ Generalized harmonic functions of Riemannian manifolds with ends ⋮ On solvability of the boundary value problems for the inhomogeneous elliptic equations on noncompact Riemannian manifolds ⋮ On the solvability of boundary value problems for the stationary Schrödinger equation in unbounded domains on Riemannian manifolds

Cites Work

• Uniformly elliptic operators on Riemannian manifolds
• Positive harmonic functions on complete manifolds of negative curvature
• Nonlinear analysis in geometry
• On the Dirichlet Problem at Infinity for Manifolds of Nonpositive Curvature
• Harmonic functions on complete riemannian manifolds
• Elliptic Partial Differential Equations of Second Order
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Some criteria for parabolicity and hyperbolicity of the boundary sets of surfaces
• Elliptic partial differential equations on the warped products of riemannian manifolds
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