Oscillation and nonoscillation criteria for second order quasilinear differential equations

1997 ◽  
Vol 76 (1-2) ◽  
pp. 81-99 ◽  
Author(s):  
T. Kusano ◽  
Y. Naito
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation

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.

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 for Differential Equations with 𝑝-Laplacian

2007 ◽  
Vol 14 (2) ◽  
pp. 239-252
Author(s):  
Miroslav Bartušek ◽  
Mariella Cecchi ◽  
Zuzana Došlá ◽  
Mauro Marini
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Oscillatory Solution ◽  
Second Order ◽  
Asymptotic Estimates ◽  
Nonoscillatory Solutions ◽  
Order Nonlinear Differential Equation ◽  
Monotonicity Properties ◽  
Oscillation And Nonoscillation

Abstract The existence of at least one oscillatory solution of a second order nonlinear differential equation with 𝑝-Laplacian is considered. The global monotonicity properties and asymptotic estimates for nonoscillatory solutions are investigated as well.

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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