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Oscillation Criteria of Comparison Type for Nonlinear Functional Differential Equations
Author(s) -
Grace S. R.
Publication year - 1995
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.19951730112
Subject(s) - mathematics , oscillation (cell signaling) , nonlinear system , differential equation , functional differential equation , mathematical analysis , type (biology) , order (exchange) , function (biology) , functional equation , mathematical physics , physics , quantum mechanics , ecology , economics , biology , genetics , finance , evolutionary biology
In this paper we relate the oscillation problem of the nonlinear functional differential equation ( a ( t ) x' ( t )) ' + q ( t ) f ( x ( g ( t )))= 0 and the nonlinear neutral functional differential equation ( a ( t ) ( x ( t ) + p ( t ) x (g * ( t )))'} + q ( t ) f ( x ( g ( t ))) = 0 to some linear second order ordinary differential equations. Recent results on linear oscillation can thus be used to obtain interesting oscillation criteria for the nonlinear equations. Similar results for the forced nonlinear functional differential equation ( a ( t ) x' ( t )) ' + q ( t ) f ( x ( g ( t ))) = e ( t ) and the forced neutral functional differential equation ( a ( t ) ( x ( t ) + mx ( t — n ))')' + q ( t ) f ( x ( g ( t ))) = e ( t ) are also established. The function f appeared in the above equations is not require to be monotone.