Some properties of solutions to a planar system of nonlinear differential equations

Abstract

In this paper we present for the solutions of a planar system of differential equations, extremal principle, Nicolescu-type and Butlewski-type separation theorems. Some applications and examples are given.

Authors

V. Ilea
(Babes Bolyai Univ.)

D. Otrocol
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy,

Keywords

Nonlinear second order differential system; extremal principle; zeros of solutions; Sturm-type theorem; Nicolescu-type theorem; Butlewski-type theorem

Cite this paper as:

V. Ilea, D. Otrocol, Some properties of solutions to a planar system of nonlinear differential equations, Studia Univ. Babes-Bolyai Math., 63 (2018) no. 2, pp. 225-234.
doi: 10.24193/subbmath.2018.2.06

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About this paper

Journal

Studia Universitatis Babes-Bolyai Mathematica

Publisher Name

Univ. Babes-Bolyai, Romania

Print ISSN

0252-1938

Online ISSN

2065-961X

MR

MR3819870

ZBL

Google Scholar

References

Paper in html format

References

[1] Butlewski, Z., Sur les zeros des integrales reelles des equations differentielles lineaires, Mathematica, 17(1941), 85-110.

[2] Hartman, P., Ordinary differential equations, J. Wiley and Sons, New York, 1964.

[3] Ilea, V.A., Otrocol, D., Rus, I.A., Some properties of solutions of the homogeneous nonlinear second order differential equations, Mathematica, 57(80)(2017), no. 1-2, 38- 43.

[4] Muresan, A.S., Tonelli’s lemma and applications, Carpathian J. Math., 28(2012), no. 1, 103-110.

[5] Nicolescu, M., Sur les theoremes de Sturm, Mathematica, 1(1929), 111-114.

[6] Reid, W.T., Sturmian theory for ordinary differential equations, Springer, Berlin, 1980.

[7] Rus, I.A., On the zeros of solutions of a system with two first order differential equations, (Romanian), Studii si Cercetari de Matematica (Cluj), 14(1963), 151-156.

[8] Rus, I.A., Separation theorems for the zeros of some real functions, Mathematica, 27(1985), no. 1, 43-46.

[9] Rus, I.A., Differential equations, integral equations and dinamical systems, (Romanian), Transilvania Press, Cluj-Napoca, 1996.

[10] Sansone, G., Equazioni differenziali nel compo reale, Parte Prima, Bologna, 1948.

[11] Sansone, G., Equazioni differenziali nel compo reale, Parte Seconda, Bologna, 1949.

[12] Swanson, C.A., Comparison and oscillation theory of linear differential equations, Academic Press, New York, 1968.

[13] Tonelli, L., Un’osservazione su un teorema di Sturm, Boll. Union. Mat. Italiana, 6(1927), 126-128.

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