The Schrodinger-Type Equation on Higher Dimensional Riemannian Manifolds

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概要

• 論文の詳細を見る

• We consider the equation -Δu+qu=λu on noncompact Riemannian manifolds having the metric [numerical formula], where λ is an arbitrary positive constant. In regard to the non-existence of L^2-solutions, known results have long been only of two types. The one was in the case of small ρ^<11>(r) and the other for two-dimensional manifolds. This article extends the latter to higher dimensional manifolds by reducing the problem to an ordinary differential equation. The proof is carried out without assuming the continuity of the solution.

• 明治大学の論文

著者

• 今野 礼二

  School Of Science And Technology Meiji University

• 飯山 祐子

  School of Science and Technology, Meiji University

• 森谷 亜希子

  School of Science and Technology, Meiji University

• 飯山 祐子

  School Of Science And Technology Meiji University

• 森谷 亜希子

  School Of Science And Technology Meiji University

関連論文

• The Schrodinger-Type Equation on Higher Dimensional Riemannian Manifolds
• Radial Solutions to the Helmholtz-Type Equation on Riemannian Manifolds
• On Positive Eigenvalues of the Schrödinger Operators with Unbounded Potentials
• 球対称なリ-マン多様体における-△u+qu=λuの解の漸近挙動
• 球対称なリーマン多様体における-Δu+qu=λuの解の漸近挙動
• 回転面上のラプラス・ベルトラミ作用素の固有関数の評価
• 一般領域における-Δの正固有値について
• 回転面上のラプラス・ベルトラミ作用素の固有関数の評価
• 一般領域における-Δの正固有値について

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