Critical oscillation constant for half-linear differential equations with periodic coefficients

2010 ◽  
Vol 190 (3) ◽  
pp. 395-408 ◽  
Author(s):  
Ondřej Došlý ◽  
Petr Hasil
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Periodic Coefficients ◽  
Linear Differential ◽  
Critical Oscillation ◽  
Oscillation Constant

scholarly journals Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values

2018 ◽  
Vol 16 (1) ◽  
pp. 507-521 ◽  
Author(s):  
Petr Hasil ◽  
Michal Veselý
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Qualitative Theory ◽  
Linear Differential Equations ◽  
Power Functions ◽  
Mean Values ◽  
Linear Differential ◽  
Critical Oscillation ◽  
Non Linear Equations ◽  
Oscillation Constant

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.

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.

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