# Some properties of solutions of the homogeneous nonlinear second order differential equations

## 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

## PDF

2016-Ilea-Otrocol-Rus-Some properties of solutions.pdf ??

Mathematica

1222-9016

2601-744X

MR3611700