OSCILLATION OF SOLUTIONS TO SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS OF GENERALIZED EULER TYPE

被引：0

作者：

Aghajani, Asadollah ^{[1
]}

O'regan, Donal ^{[2
]}

Roomi, Vahid ^{[1
]}

机构：

[1] Iran Univ Sci & Tech, Sch Math, Tehran, Iran

[2] Natl Univ Ireland, Sch Math Stat & Applied Math, Galway, Ireland

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年

关键词：

Oscillation; nonlinear differential equations; Lienard system; LIENARD EQUATIONS; THEOREMS; SYSTEM;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with the oscillatory behavior of the solutions of a generalized Euler differential equation where the nonlinearities satisfy smoothness conditions which guarantee the uniqueness of solutions of initial value problems, however, no conditions of sub(super) linearity are assumed. Some implicit necessary and sufficient conditions and some explicit sufficient conditions are given for all nontrivial solutions of this equation to be oscillatory or nonoscillatory. Also, it is proved that solutions of the equation are all oscillatory or all nonoscillatory and cannot be both.

引用

页数：13

共 26 条

[1] Agarwal RP., 2012, DYNAM CONT DIS SER A, V18, P267
[2] On the homoclinic orbits of the generalized Lienard equations
Aghajani, A.
Moradifam, A.
[J]. APPLIED MATHEMATICS LETTERS, 2007, 20 (03) : 345 - 351
[3] On the property of (X+) for generalised Lienard system
Aghajani, A.
Roomi, V.
[J]. INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS, 2008, 1 (04) : 276 - 282
[4] Oscillation theorems for the generalized Lienard system
Aghajani, A.
Jalilian, Y.
Roomi, V.
[J]. MATHEMATICAL AND COMPUTER MODELLING, 2011, 54 (9-10) : 2471 - 2478
[5] THE GENERALISED LIENARD EQUATIONS
Aghajani, A.
Moradifam, A.
[J]. GLASGOW MATHEMATICAL JOURNAL, 2009, 51 : 605 - 617
[6] Oscillation of solutions of second-order nonlinear differential equations of Euler type
Aghajani, A.
Moradifm, A.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 326 (02) : 1076 - 1089
[7] An oscillation theorem for second-order nonlinear differential equations of Euler type
Aghajani, Asadollah
Roomi, Vahid
[J]. TURKISH JOURNAL OF MATHEMATICS, 2012, 36 (02) : 273 - 280
[8] Atkinson F. V., 1955, PAC J MATH, V5, P643
[9] Cronin J., 2007, ORDINARY DIFFERENTIA
[10] Grace S. R., 1987, B I MATH ACAD SINICA, V15

← 1 2 3 →