Asymptotics of eigenvalues of A regular boundary-value problem
We study a boundary-value problem x (n) + Fx = λx, U h(x) = 0, h = 1,..., n, where functions x are given on the interval [0, 1], a linear continuous operator F acts from a Hölder space H y into a Sobolev space W 1 n+s , U h are linear continuous functional defined in the space \(H^{k_h } \) , and...
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| Date: | 1996 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1996
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5313 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We study a boundary-value problem x (n) + Fx = λx, U h(x) = 0, h = 1,..., n, where functions x are given on the interval [0, 1], a linear continuous operator F acts from a Hölder space H y into a Sobolev space W 1 n+s , U h are linear continuous functional defined in the space \(H^{k_h } \) , and k h ≤ n + s - 1 are nonnegative integers. We introduce a concept of k-regular-boundary conditions U h(x)=0, h = 1, ..., n and deduce the following asymptotic formula for eigenvalues of the boundary-value problem with boundary conditions of the indicated type: \(\lambda _v = \left( {i2\pi v + c_ \pm + O(|v|^\kappa )} \right)^n \) , v = ± N, ± N ± 1,..., which is true for upper and lower sets of signs and the constants κ≥0 and c ± depend on boundary conditions. |
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