Abstract
In this paper we consider the following nonlinear homogeneous second order differential equations, \(F(x,y,y^{\prime},y^{\prime\prime})=0.\) We present for the solutions, \(y\in C^2[a,b]\), of this equation, extremal principle, Sturm-type, Nicolescu-type and Butlewski-type separation theorems.
Some applications and examples are given. Open problems are also presented.
Authors
V. Ilea
(Babes Bolyai Univ)
D. Otrocol
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)
I.A. Rus
(Babes Bolyai Univ.)
Keywords
Homogeneous nonlinear second order differential equation, zeros of solutions, Sturm-type theorem, Nicolescu-type theorem, Butlewski-type theorem, bilocal problem, Cauchy problem, open problem, extremal principle.
Cite this paper as:
V. Ilea, D. Otrocol, I. A. Rus, Some properties of solutions of the homogeneous nonlinear second order differential equations, Mathematica, 57 (80) (2015), no 1-2, pp. 38-43
2016-Ilea-Otrocol-Rus-Some properties of solutions.pdf ??
About this paper
Journal
Mathematica
Publisher Name
Romanian Academy Publishing House
DOI
Paper on journal website
http://math.ubbcluj.ro/~mathjour/articles/2015/ilea-otrocol-rus.pdf
Print ISSN
1222-9016
Online ISSN
2601-744X
MR
MR3611700
ZBL
Google Scholar
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