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A Comparison Theorem for a Second Order Linear Quasi‐Differential Equation
Author(s) -
O'Hara J. G.
Publication year - 1996
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/53.1.118
Subject(s) - mathematics , order (exchange) , differential equation , linear differential equation , homogeneous differential equation , line (geometry) , mathematical analysis , differential (mechanical device) , comparison theorem , real line , pure mathematics , ordinary differential equation , physics , geometry , differential algebraic equation , finance , economics , thermodynamics
We are concerned with the non‐oscillatory behaviour of a second order linear quasi‐differential equation defined a.e. over a half‐line. More particularly given that ( py ′)′ + qy = 0 is non‐oscillatory we show that by writing q in a form which is amenable to further analysis we can generalise Sturm's comparison theorem.