Critical Oscillation Constant for Half Linear Differential Equations Which Have Different Periodic Coefficients

Year 2016, Volume: 29 Issue: 1, 79 - 86, 21.03.2016

Adil Mısır Banu Mermerkaya

Abstract

In this paper, we compute explicitly the oscillation constant for certain half-linear second-order differential equations which have different periodic coefficients. If the periods of these functions are coincide, our results reduce to Dosly and Hasil's results, which were published in Annali di Matematica 190 (2011) 395--408. Finally some examples are also given to illustrate the results.

Keywords

Half-linear differential equation, Euler equation, Riemann-Weber equation, Prüfer transformation, Critical oscillation constant

References

• Beesack, P. R., Hardy’s inequality and its extensions. Pac. J. Math (1961) 11 (1), 39-61.
• Bihari, I., An oscillation theorem concerning the half-linear differential equation of second order. Magy. Tud. Akad. Mat. Kut. Intez. Közl. (1964) 8, 275-280. [3] Dosly, O., Perturbations of the half-linear Euler-Weber type differential equation. J. Math. Anal. Appl. (2006) 323, 426-440.
• Dosly, O., Hasil, P., Critical oscillation constant for half-linear differential equations with periodic coefficients. Ann. Math. Pur. App. (2011) 190 (3), 395-408.
• Dosly, O., Rehak, P. Half-linear Differential Equations. Elsevier Amsterdam (2005).
• Elbert, A., Schneider, A., Perturbations of the half-linear Euler differential equation. Results. Math. (2000) 37(1-2), 56-83.
• Hasil, P., Conditional oscillation of half-linear differential equations with periodic coefficients. Arch. Math. (2008) 44(2), 119-131.
• Schmidt, K. M., Oscillation of the perturbed Hill equation and the lower spectrum of radially periodic Schrödinger operators in the plane. Proc. Amer. Math. Soc. (1999) 127(8), 2367-2374.
• Schmidt, K. M., Critical coupling constant and eigenvalue Sturm-Liouville operators, Commun. Math. Phys. (2000) 211, 465-485. perturbed periodic