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Non‐existence of large eigenvalues of a third order differential equation
Author(s) -
Davis A. M. J.
Publication year - 1978
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300009372
Subject(s) - mathematics , eigenvalues and eigenvectors , differential equation , order (exchange) , third order , mathematical analysis , characteristic equation , first order partial differential equation , fourier transform , linear differential equation , homogeneous differential equation , universal differential equation , exact differential equation , ordinary differential equation , law , quantum mechanics , physics , differential algebraic equation , finance , political science , economics
Summary The study of plasma instabilities has led to the question whether a certain third order linear differential equation involving a parameter p has solutions which vanish as x → ± ∞. Assuming existence, it is first easily shown that Rep must be positive and then, after a Fourier transform has changed the equation to one of second order, standard comparison equation techniques are used to obtain a contradiction, valid for large enough p .
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