oscillation constant
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2018 ◽  
Vol 16 (1) ◽  
pp. 507-521 ◽  
Author(s):  
Petr Hasil ◽  
Michal Veselý

AbstractThe paper belongs to the qualitative theory of half-linear equations which are located between linear and non-linear equations and, at the same time, between ordinary and partial differential equations. We analyse the oscillation and non-oscillation of second-order half-linear differential equations whose coefficients are given by the products of functions having mean values and power functions. We prove that the studied very general equations are conditionally oscillatory. In addition, we find the critical oscillation constant.


2017 ◽  
Vol 15 (1) ◽  
pp. 548-561 ◽  
Author(s):  
Adil Misir ◽  
Banu Mermerkaya

Abstract In this paper, we compute explicitly the oscillation constant for certain half-linear second-order differential equations having different periodic coefficients. Our result covers known result concerning half-linear Euler type differential equations with α—periodic positive coefficients. Additionally, our result is new and original in case that the least common multiple of these periods is not defined. We give an example and corollaries which illustrate cases that are solved with our result.


2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Adil Misir ◽  
Banu Mermerkaya

We compute explicitly the oscillation constant for Euler type half-linear second-order differential equation having multi-different periodic coefficients.


2016 ◽  
Vol 53 (1) ◽  
pp. 22-41
Author(s):  
Jaroslav Jaroš ◽  
Michal Veselý

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.


2014 ◽  
Vol 51 (3) ◽  
pp. 303-321
Author(s):  
Petr Hasil ◽  
Michal Veselý

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.


2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Petr Hasil ◽  
Robert Mařík ◽  
Michal Veselý

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.


2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Petr Hasil ◽  
Michal Veselý

We investigate a type of the Sturm-Liouville difference equations with almost periodic coefficients. We prove that there exists a constant, which is the borderline between the oscillation and the nonoscillation of these equations. We compute this oscillation constant explicitly. If the almost periodic coefficients are replaced by constants, our result reduces to the well-known result about the discrete Euler equation.


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