Existence of Oscillatory Solutions of Second Order Functional Equations with Damping Terms

2011 ◽  
pp. 461-464
Keyword(s):  
Functional Equations ◽  
Second Order ◽  
Oscillatory Solutions

Change of Variables in Factorization Method for Second-order Functional Equations

2004 ◽  
Vol 54 (11) ◽  
pp. 1257-1263 ◽  
Author(s):  
Alina Dobrogowska ◽  
Tomasz Goliński ◽  
Anatol Odzijewicz
Keyword(s):  
Functional Equations ◽  
Factorization Method ◽  
Second Order ◽  
Change Of Variables

scholarly journals Kamenev-Type Oscillation Criteria for the Second-Order Nonlinear Dynamic Equations with Damping on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
M. Tamer Şenel
Keyword(s):  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Sufficient Conditions ◽  
Second Order ◽  
Oscillatory Solutions ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Dynamic Equations ◽  
Generalized Riccati Transformation ◽  
Type Oscillation

The oscillation of solutions of the second-order nonlinear dynamic equation(r(t)(xΔ(t))γ)Δ+p(t)(xΔ(t))γ+f(t,x(g(t)))=0, with damping on an arbitrary time scaleT, is investigated. The generalized Riccati transformation is applied for the study of the Kamenev-type oscillation criteria for this nonlinear dynamic equation. Several new sufficient conditions for oscillatory solutions of this equation are obtained.

Necessary and sufficient conditions for asymptotic decay of oscillations in delayed functional equations

1981 ◽  
Vol 91 (1-2) ◽  
pp. 135-145
Author(s):  
Lu-San Chen ◽  
Cheh-Chih Yeh
Keyword(s):  
Differential Operator ◽  
Functional Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Oscillatory Solutions ◽  
Asymptotic Decay ◽  
Image Position ◽  
Necessary And Sufficient

SynopsisThis paper studies the equationwhere the differential operator Ln is defined byand a necessary and sufficient condition that all oscillatory solutions of the above equation converge to zero asymptotically is presented. The results obtained extend and improve previous ones of Kusano and Onose, and Singh, even in the usual case wherewhere N is an integer with l≦N≦n–1.

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