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.

Conditional oscillation of Riemann-Weber half-linear differential equations with asymptotically almost periodic coefficients

2014 ◽  
Vol 51 (3) ◽  
pp. 303-321
Author(s):  
Petr Hasil ◽  
Michal Veselý
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Almost Periodic ◽  
Periodic Coefficients ◽  
Conditional Oscillation ◽  
Linear Differential ◽  
Asymptotically Almost Periodic ◽  
Oscillation Constant

We analyse the oscillation and non-oscillation of second-order half-linear differential equations with periodic and asymptotically almost periodic coefficients, where the equations have the so-called Riemann-Weber form. For these equations, we find an explicit oscillation constant. Corollaries and examples are mentioned as well.

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

Nonprincipal solutions in oscillation criteria for half-linear differential equations

2010 ◽  
Vol 47 (1) ◽  
pp. 127-137
Author(s):  
Ondřej Došlý ◽  
Jana Řezníčková
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Second Order ◽  
Oscillation Criterion ◽  
Linear Differential Equations ◽  
Integral Term ◽  
Oscillation Criteria ◽  
Second Order Differential Equation ◽  
Linear Differential

We establish a new oscillation criterion for the half-linear second order differential equation \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$(r(t)\Phi (x'))' + c(t)\Phi (x) = 0,\Phi (x): = |x|^{p - 2} x,p > 1.$$ \end{document} In this criterion, an integral term appears which involves a nonprincipal solution of a certain equation associated with (*).

scholarly journals Conditional Oscillation of Half-Linear Differential Equations with Coefficients Having Mean Values

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Petr Hasil ◽  
Robert Mařík ◽  
Michal Veselý
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Linear Differential Equations ◽  
Almost Periodic ◽  
Mean Values ◽  
Conditional Oscillation ◽  
The Mean ◽  
Linear Differential ◽  
Positive Coefficients ◽  
Oscillation Constant

We prove that the existence of the mean values of coefficients is sufficient for second-order half-linear Euler-type differential equations to be conditionally oscillatory. We explicitly find an oscillation constant even for the considered equations whose coefficients can change sign. Our results cover known results concerning periodic and almost periodic positive coefficients and extend them to larger classes of equations. We give examples and corollaries which illustrate cases that our results solve. We also mention an application of the presented results in the theory of partial differential equations.

An Oscillation Criterion for nth Order Non-Linear Differential Equations with Functional Arguments

1983 ◽  
Vol 26 (1) ◽  
pp. 35-40 ◽  
Author(s):  
S. R. Grace ◽  
B. S. Lalli
Keyword(s):  
Differential Equations ◽  
Order Equation ◽  
Second Order ◽  
Oscillation Criterion ◽  
Linear Differential Equations ◽  
Non Linear ◽  
Even Order ◽  
Linear Differential

AbstractAn oscillation criterion for an even order equation: x(n) + q(t)ƒ(x(t)), x[g(t)]) = 0 is provided. This criterion is an extension of a result established by Yeh for the second order equation ẍ + q(t)ƒ(x(t)), x[g(t)]) = 0.

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