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Oscillation criteria for fourth‐order differential equations with middle term
Author(s) -
Amara Jamel Ben
Publication year - 2012
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.200910082
Subject(s) - mathematics , oscillation (cell signaling) , term (time) , differential equation , order (exchange) , mathematical analysis , exponential function , differential (mechanical device) , exponential growth , oscillation theory , linear differential equation , physics , exact differential equation , quantum mechanics , genetics , finance , economics , biology , thermodynamics
Oscillation criteria for self‐adjoint fourth‐order differential equations\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty} $$ (r(x)y^{\prime \prime })^{\prime \prime }-(q(x)y^{\prime })^{\prime }= p(x)y $$ \end{document} were established for various conditions on the coefficients r ( x ) > 0, q ( x ) and p ( x ). However, most of these results deal with the case when lim x → ∞ ∫ x 1 q ( s ) ds < +∞. In this note we give a new oscillation criterion in the case when this condition is not fulfilled, in particular when q ( x )↗ + ∞ (even with exponential growth).