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Half‐Linear Eigenvalue Problems
Author(s) -
Eberhard Walter,
Elbert Árpad
Publication year - 1997
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19971830105
Subject(s) - mathematics , eigenvalues and eigenvectors , wkb approximation , mathematical analysis , boundary value problem , boundary (topology) , constant (computer programming) , differential equation , physics , quantum mechanics , computer science , programming language
We consider the eigenvalue problemfor t ϵ [0, b ], where a n = | a | n sgn a, a ϵ ℝ, λ ϵ ℝ, the constants μ , v are real such that 0 ≤ μ < n and derive asymptotic estimates for solutions of the differential equation in the definite case q ( t )> 0 which corresponds to the well‐known WKB‐approximation in the linear case n = 1, μ = 0. In the second part we investigate the asymptotic distribution of the eigenvalues in the general case of two ‐point boundary conditions and refine these results for the so called separated boundary conditions.