scholarly journals Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 502
Author(s):  
Zuzana Pátíková
Keyword(s):  
Differential Equations ◽  
Comparison Theorem ◽  
Type Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Comparison Theorems ◽  
Type Integral ◽  
Comparison Criteria ◽  
Linear Differential

In this paper, we present further developed results on Hille–Wintner-type integral comparison theorems for second-order half-linear differential equations. Compared equations are seen as perturbations of a given non-oscillatory equation, which allows studying the equations on the borderline of oscillation and non-oscillation. We bring a new comparison theorem and apply it to the so-called generalized Riemann–Weber equation (also referred to as a Euler-type equation).

scholarly journals Two-Point Oscillation for a Class of Second-Order Damped Linear Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Kong Xiang-Cong ◽  
Zheng Zhao-Wen
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Comparison Theorem ◽  
Second Order ◽  
Linear Differential Equations ◽  
Damping Term ◽  
Linear Differential

Using the comparison theorem, the two-point oscillation for linear differential equation with damping term is considered, where . Results are obtained that or imply the two-point oscillation of the equation.

Hille–Wintner type comparison criteria for the half-linear differential equations of third order

2014 ◽  
Vol 20 (2) ◽  
Author(s):  
Jozef Kiseľák
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Comparison Theorem ◽  
Linear Differential Equations ◽  
Third Order ◽  
Weak Property ◽  
Comparison Criteria ◽  
Linear Differential

AbstractWe obtain an analogue of the integral Hille–Wintner comparison theorem for the half-linear differential equations of third order. We also give an example involving a differential equation of Euler type, which gives a condition under which half-linear differential equations have weak property

Comparison theorems for oscillation of second-order half-linear differential equations

2006 ◽  
Vol 111 (1-2) ◽  
pp. 165-179 ◽  
Author(s):  
Jitsuro Sugie ◽  
Naoto Yamaoka
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Comparison Theorems ◽  
Linear Differential

Oscillation and Comparison Theorems for Second Order Linear Differential Equations with Integrable Coefficients

1974 ◽  
Vol 26 (02) ◽  
pp. 294-301
Author(s):  
G. Butler ◽  
J. W. Macki
Keyword(s):  
Differential Equations ◽  
Eigenvalue Problems ◽  
Second Order ◽  
Linear Differential Equations ◽  
Comparison Theorems ◽  
Standard Theory ◽  
General Hypothesis ◽  
Order Linear ◽  
Linear Differential ◽  
Image Position

The classical comparison and interlacing theorems of Sturm were originally proved for the equations under the assumption that all coefficients are real-valued, continuous, and p > 0, P > 0. Atkinson [1, Chapter 8] has carried out the standard theory for eigenvalue problems involving (1), under the more general hypothesis

scholarly journals Comparison theorems of Hille-Wintner type for third order linear differential equations

1980 ◽  
Vol 21 (2) ◽  
pp. 175-188 ◽  
Author(s):  
L. Erbe
Keyword(s):  
Differential Equations ◽  
Linear Equation ◽  
Linear Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Comparison Theorems ◽  
Third Order ◽  
Order Linear ◽  
The Third ◽  
Linear Differential

Integral comparison theorems of Hille-Wintner type of second order linear equations are shown to be valid for the third order linear equation y‴ + q(t)y = 0.

scholarly journals Use of the Modified Riccati Technique for Neutral Half-Linear Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 235
Author(s):  
Zuzana Pátíková ◽  
Simona Fišnarová
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Type Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Type Criterion ◽  
Linear Differential

We study the second-order neutral half-linear differential equation and formulate new oscillation criteria for this equation, which are obtained through the use of the modified Riccati technique. In the first statement, the oscillation of the equation is ensured by the divergence of a certain integral. The second one provides the condition of the oscillation in the case where the relevant integral converges, and it can be seen as a Hille–Nehari-type criterion. The use of the results is shown in several examples, in which the Euler-type equation and its perturbations are considered.

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