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 ??

About this paper

Journal

Mathematica

Publisher Name

Romanian Academy Publishing House

Print ISSN

1222-9016

Online ISSN

2601-744X

MR

MR3611700

ZBL

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