Some properties of the solutions of third order linear ordinary differential equations

Abstract

The method of Riccati equations is used to study some properties of third order linear ordinary differential equations. Some criteria of asymptotic behavior and non stability of solution of this equation are obtained. Two oscillatory criteria are proved. 2010 AMS Mathematics subject classification. Primary 34C10, 34C99.

On one oscillatory criterion for the second order linear ordinary differential equations

“…Abdullah [1], G.A. Grigorian [5]); the second one -which is radical -studies the oscillatory behavior of equations on the finite interval (interval oscillatory criteria: see Wong's theorem in [10], G.A. Grigorian [5], Sturm's theorem in [7], Q. Kong [9], J.G.…”

“…Oscillatory analysis of second order linear ordinary differential equations is one of the important problems in the qualitative theory of differential equations and it is the subject of numerous papers (see [16] and cited works therein [1,2,4,5,[7][8][9][10][11][12][13][14][15]17]). …”

Kamenev type conditions for oscillation of third order linear ordinary differential equations

“…The study of the oscillatory behavior of solutions to linear third-order ordinary differential equations is an important problem in the qualitative theory of differential equations, and many works are devoted to it (see [1,2,4] and the works cited therein). Among them notice the following result due to Lazer.…”

Properties of solutions of matrix Riccati equations

“…In the scalar (n = 1) and the quaternionic cases some properties of t 1 -regular solutions of Eq. (1.1) are studied in [4][5][6][7][8][9] and are used to qualitative study of some linear ordinary differential equations and systems of such equations (see [10][11][12][13][14][15][16]).…”