頁籤選單縮合
題 名 | On the Multiplicity of the Eigenvalues of the Vectorial Sturm-Liouville Equation |
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作 者 | Lin, Chien-wen; | 書刊名 | Tamkang Journal of Mathematics |
卷 期 | 42:3 2011.秋[民100.秋] |
頁 次 | 頁265-274 |
分類號 | 313.1 |
關鍵詞 | |
語 文 | 英文(English) |
英文摘要 | LetQ(x) be a continuous m×m real symmetric matrix-valued function defined on [0, 1], and denote the Sturm-Liouville operator-d^2/dx^2+Q(x) as LQ with Q(x) as its potential function. In this paper we prove that for each Dirichlet eigenvalue λ(subscript ∗) of LQ, the geometric multiplicity of λ(subscript ∗) is equal to its algebraic multiplicity. Applying this result, we get a necessary and sufficiently condition such that each Dirichlet eigenvalue of L(subscript Q) is of multiplicity m. |
本系統中英文摘要資訊取自各篇刊載內容。