Electron. J. Diff. Equ., Vol. 2014 (2014), No. 214, pp. 1-10.

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

Aydin Tiryaki

The aim of this article is to give Sturm-Picone type theorems for the pair of second order nonlinear elliptic differential equations
 \hbox{div}(p_1(x)|\nabla u|^{\alpha-1}\nabla u )
 \hbox{div}(p_2(x)|\nabla v|^{\alpha-1}\nabla v )
where $|\cdot|$ denotes the Euclidean length and $\nabla= (\frac{\partial}{\partial x_1},\dots,
 \frac{\partial}{\partial x_{n}} )^{T}$ (the superscript T denotes the transpose). Our results include some earlier results and generalize to n-dimensions well-known comparison theorems given by Sturm, Picone and Leighton ]26.37] which play a key role in the qualitative behavior of solutions. By using generalization of n dimensional Leigton's comparison theorem, an oscillation result is given as an application.

Submitted July 16, 2014. Published October 14, 2014.
Math Subject Classifications: 35B05.
Key Words: Comparison theorem; Sturm-Picone theorem; half-linear equations, variational lemma; elliptic equations; oscillation.

Show me the PDF file (244 KB), TEX file, and other files for this article.

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

Return to the EJDE web page