2019
Том 71
№ 11

All Issues

Asymptotics of eigenvalues of A regular boundary-value problem

Radzievskii G. V.

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Abstract

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 hn + 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.

English version (Springer): Ukrainian Mathematical Journal 48 (1996), no. 4, pp 537-575.

Citation Example: Radzievskii G. V. Asymptotics of eigenvalues of A regular boundary-value problem // Ukr. Mat. Zh. - 1996. - 48, № 4. - pp. 483-519.

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