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Oscillation of second‐order perturbed differential equations
Author(s) -
Mustafa Octavian G.,
Rogovchenko Yuri V.
Publication year - 2005
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.200310253
Subject(s) - mathematics , monotonic function , bounded function , constructive , oscillation (cell signaling) , infinity , nonlinear system , a priori and a posteriori , mathematical analysis , differential equation , order (exchange) , a priori estimate , character (mathematics) , uniform boundedness , physics , geometry , philosophy , process (computing) , epistemology , quantum mechanics , finance , biology , computer science , economics , genetics , operating system
We give constructive proof of the existence of vanishing at infinity oscillatory solutions for a second‐order perturbed nonlinear differential equation. In contrast to most results reported in the literature, we do not require oscillatory character of the associated unperturbed equation, monotonicity of nonlinearity, and we establish global existence of oscillatory solutions without assuming it a priori. Furthermore, as our example demonstrates, existence of bounded oscillatory solutions does not exclude existence of unbounded nonoscillatory solutions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)