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Interval oscillation criteria for second order super‐half linear functional differential equations with delay and advanced arguments
Author(s) -
Zafer A.
Publication year - 2009
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.200610801
Subject(s) - mathematics , sign (mathematics) , oscillation (cell signaling) , interval (graph theory) , order (exchange) , functional differential equation , image (mathematics) , sequence (biology) , differential equation , mathematical analysis , real number , combinatorics , computer science , genetics , finance , artificial intelligence , economics , biology
Sufficient conditions are established for oscillation of second order super half linear equations containing both delay and advanced arguments of the formwhere ϕ δ ( u ) = | u | δ –1 u ; α > 0, β ≥ α , and γ ≥ α are real numbers; k , p , q , e , τ , σ are continuous real‐valued functions; τ ( t ) ≤ t and σ ( t ) ≥ t with lim t →∞ τ ( t ) = ∞. The functions p ( t ), q ( t ), and e ( t ) are allowed to change sign, provided that p ( t ) and q ( t ) are nonnegative on a sequence of intervals on which e ( t ) alternates sign. As an illustrative example we show that every solution ofis oscillatory provided that either m 1 or m 2 or r 0 is sufficiently large (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)