A sharp oscillation criterion for second-order half-linear advanced differential equations

2021 ◽  
Vol 163 (2) ◽  
pp. 552-562
Author(s):  
G. E. Chatzarakis ◽  
S. R. Grace ◽  
I. Jadlovská
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Oscillation Criterion

Oscillation of Second-Order Nonlinear Differential Equations

2014 ◽  
Vol 548-549 ◽  
pp. 1007-1010
Author(s):  
Qing Zhu ◽  
Zhi Bin Ma
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Order Nonlinear Differential Equation

A new oscillation criterion is established for a certain class of second-order nonlinear differential equation x"(t)-b(t)x'(t)+c(t)g(x)=0, x"(t)+c(t)g(x)=0 that is different from most known ones. Some applications of the result obtained are also presented. Our results are sharper than some previous ones.

An Improved Wintner Oscillation Criterion for Second Order Linear Differential Equations

1984 ◽  
Vol 27 (1) ◽  
pp. 117-121
Author(s):  
George W. Johnson ◽  
Jurang Yan
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Linear Differential Equations ◽  
Iterative Technique ◽  
Oscillation Theorem ◽  
Order Linear ◽  
Linear Differential ◽  
Image Position

AbstractAn iterative technique is used to establish an oscillation theorem for the equation x″+ a(t)x=0 which relaxes the condition that a(t) satisfywithout the restriction that

A Second Order Superlinear Oscillation Criterion

1984 ◽  
Vol 27 (1) ◽  
pp. 102-112 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Oscillation Result ◽  
Special Case

AbstractA new oscillation criterion is given for general superlinear ordinary differential equations of second order of the form x″(t)+ a(t)f[x(t)]=0, where a ∈ C([t0∞,)), f∈C(R) with yf(y)>0 for y≠0 and and f is continously differentiable on R-{0} with f'(y)≥0 for all y≠O. In the special case of the differential equation (γ > 1) this criterion leads to an oscillation result due to Wong [9].

scholarly journals A New Oscillation Criterion for Forced Second-Order Quasilinear Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Shao Jing
Keyword(s):  
Differential Equation ◽  
Variational Principle ◽  
Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Generalized Variational Principle ◽  
Quasilinear Differential Equation ◽  
Riccati Technique ◽  
Forcing Term

By using the generalized variational principle and Riccati technique, a new oscillation criterion is established for second-order quasilinear differential equation with an oscillatory forcing term, which improves and generalizes some of new results in the literature.

Conditional oscillation of Euler type half-linear differential equations with unbounded coefficients

2016 ◽  
Vol 53 (1) ◽  
pp. 22-41
Author(s):  
Jaroslav Jaroš ◽  
Michal Veselý
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Linear Differential Equations ◽  
Unbounded Coefficients ◽  
Conditional Oscillation ◽  
Linear Differential ◽  
Oscillation Constant ◽  
Oscillatory Properties

The oscillatory properties of half-linear second order Euler type differential equations are studied, where the coefficients of the considered equations can be unbounded. For these equations, we prove an oscillation criterion and a non-oscillation one. We also mention a corollary which shows how our criteria improve the known results. In the corollary, the criteria give an explicit oscillation constant.

scholarly journals Qualitative Behavior of Solutions of Second Order Differential Equations

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 777 ◽  
Author(s):  
Clemente Cesarano ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Qualitative Behavior ◽  
Second Order Differential Equations ◽  
Future Developments ◽  
Correct Direction ◽  
Riccati Substitution ◽  
Delay Differential ◽  
The Right

In this work, we study the oscillation of second-order delay differential equations, by employing a refinement of the generalized Riccati substitution. We establish a new oscillation criterion. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. We illustrate the results with some examples.

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