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Half-Linear Eigenvalue Problems

✍ Scribed by Walter Eberhard; Árpad Elbert

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
635 KB
Volume
183
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We consider the eigenvalue problem
magnified image
for 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.

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