The aim of this article is to give Sturm-Picone type theorems for the pair of second order nonlinear elliptic differential equations
where denotes the Euclidean length and (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.
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| Aydin Tiryaki |
Department of Mathematics and Computer Sciences
Faculty of Arts and Sciences, Izmir University
35350 Uckuyular, Izmir, Turkey
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