Asymptotic Analysis of a Nonlinear Eigenvalue Problem Arising in the Waveguide Theory
- Авторлар: Valovik D.V.1, Tikhov S.V.1
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Мекемелер:
- Penza State University
- Шығарылым: Том 55, № 12 (2019)
- Беттер: 1554-1569
- Бөлім: Ordinary Differential Equations
- URL: https://journal-vniispk.ru/0012-2661/article/view/155283
- DOI: https://doi.org/10.1134/S0012266119120036
- ID: 155283
Дәйексөз келтіру
Аннотация
We consider a nonlinear eigenvalue problem for a system of ordinary differential equations arising in the waveguide theory. The nonlinearity is characterized by two nonnegative parameters α and β. For α = β = 0, we arrive at a linear problem that has finitely many (positive) eigenvalues. It is proved that for α > 0 and β ≥ 0 there exist infinitely many positive eigenvalues; their asymptotics is indicated. It is also proved that for α = 0 and β > 0 there exist finitely many eigenvalues. A comparison theorem for the eigenvalues is obtained for α, βs > 0. It is shown that perturbation theory methods cannot be used to study the nonlinear problem completely.
Авторлар туралы
D. Valovik
Penza State University
Хат алмасуға жауапты Автор.
Email: dvalovik@mail.ru
Ресей, Penza, 440026
S. Tikhov
Penza State University
Хат алмасуға жауапты Автор.
Email: tik.stanislav2015@yandex.ru
Ресей, Penza, 440026
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