Acta mathematica scientia, Series B >
PROPERTY (X+) FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS OF GENERALIZED EULER TYPE
Received date: 2011-06-08
Revised date: 2013-01-21
Online published: 2013-09-20
In this paper the generalized nonlinear Euler differential equation t2k(tu´)u´´+t(f(u) + k(tu´))u´ + g(u) = 0 is considered. Here the functions f(u), g(u) and k(u) sat-isfy smoothness conditions which guarantee the uniqueness of solutions of initial value problems, however, no conditions of sub(super) linearity are assumed. We present some necessary and sufficient conditions and some tests for the equivalent planar system to have or fail to have property (X+), which is very important for the existence of periodic solutions and oscillation theory.
Key words： property (X+); nonlinear differential equations; Li´enard system
Asadollah AGHAJANI , Vahid ROOMI . PROPERTY (X+) FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS OF GENERALIZED EULER TYPE[J]. Acta mathematica scientia, Series B, 2013 , 33(5) : 1398 -1406 . DOI: 10.1016/S0252-9602(13)60091-0
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