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Classification of second‐order linear differential equations and an application to singular elliptic eigenvalue problems
Author(s) -
Naito Yūki
Publication year - 2012
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdr117
Subject(s) - mathematics , eigenvalues and eigenvectors , linear differential equation , mathematical analysis , differential equation , elliptic partial differential equation , oscillation (cell signaling) , order (exchange) , constant (computer programming) , physics , finance , quantum mechanics , biology , computer science , economics , genetics , programming language
We consider conditionally oscillatory second‐order linear differential equations with a parameter, and investigate the asymptotic behaviour and number of zeros of solutions to the equations. In particular, we find criteria for the equations to be oscillatory/nonoscillatory when the parameter is on the oscillation constant. We also show an application to singular elliptic eigenvalue problems on a ball in R N .