Oscillation and Nonoscillation Criteria for a Second Order Linear Equation

1999 ◽  
Vol 6 (5) ◽  
pp. 401-414
Author(s):  
T. Chantladze ◽  
N. Kandelaki ◽  
A. Lomtatidze
Keyword(s):  
Linear Equation ◽  
Integrable Function ◽  
Second Order ◽  
Order Linear ◽  
Locally Integrable Function ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation

Abstract New oscillation and nonoscillation criteria are established for the equation 𝑢″ + 𝑝(𝑡)𝑢 = 0, where 𝑝 : ]1, + ∞[ → 𝑅 is the locally integrable function. These criteria generalize and complement the well known criteria of E. Hille, Z. Nehari, A. Wintner, and P. Hartman.

On Oscillation and Nonoscillation of a Second Order Half-Linear Equation

2000 ◽  
Vol 7 (2) ◽  
pp. 329-346 ◽  
Author(s):  
N. Kandelaki ◽  
A. Lomtatidze ◽  
D. Ugulava
Keyword(s):  
Linear Equation ◽  
Second Order ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation

Abstract New oscillation and nonoscillation criteria are established for the equation u″ + p(t)|u| α |u′|1–α sgn u = 0, where α ∈]0, 1] and the function p :]0, +∞[→] – ∞, +∞[ is locally integrable.

Oscillation and Nonoscillation Criteria for Second-Order Linear Differential Equations

1997 ◽  
Vol 4 (2) ◽  
pp. 129-138
Author(s):  
A. Lomtatidze
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation

Abstract Sufficient conditions for oscillation and nonoscillation of second-order linear equations are established.

Weighted Averaging Techniques in Oscillation Theory for Second Order Difference Equations

1992 ◽  
Vol 35 (1) ◽  
pp. 61-69 ◽  
Author(s):  
Lynn H. Erbe ◽  
Pengxiang Yan
Keyword(s):  
Oscillation Theory ◽  
Second Order ◽  
Weighted Averaging ◽  
Real Numbers ◽  
Order Difference ◽  
The Matrix ◽  
System 2 ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation ◽  
Averaging Techniques

AbstractWe consider the self-adjoint second-order scalar difference equation (1) Δ(rnΔxn) +pnXn+1 = 0 and the matrix system (2) Δ(RnΔXn) + PnXn+1 = 0, where are seQuences of real numbers (d x d Hermitian matrices) with rn > 0(Rn > 0). The oscillation and nonoscillation criteria for solutions of (1) and (2), obtained in [3, 4, 10], are extended to a much wider class of equations by Riccati and averaging techniques.

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