Electron. J. Diff. Equ., Vol. 2014 (2014), No. 146, pp. 1-11.

Sturm-Picone type theorems for second-order nonlinear differential equations

Aydin Tiryaki

Abstract:
The aim of this article is to give Sturm-Picone type theorems for the pair of second-order nonlinear differential equations
$$\displaylines{ (p_1(t)|x'|^{\alpha-1}x')'+q_1(t)f_1(x)=0 \cr (p_2(t)|y'|^{\alpha-1}y')'+q_2(t)f_2(y)=0,\quad t_1<t<t_2 }$$
in both regular and singular cases. Our results include some earlier results and generalize the well-known comparison theorems given by Sturm [19], Picone [18] and Leighton [5] which play a key role in the qualitative behaviour of the solutions.

Submitted March 5, 2014. Published June 20, 2014.
Math Subject Classifications: 34C10, 34C15.
Key Words: Comparison theorem; Sturm-Picone theorem; half-linear; second order differential equations; singular equation; variational lemma.

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Aydin Tiryaki
Department of Mathematics and Computer Sciences
Faculty of Arts and Sciences, Izmir University
35350 Uckuyular, Izmir, Turkey
email: aydin.tiryaki@izmir.edu.tr

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