TY  - JOUR
ID  - Elabbasy2011
LB  - Elabbasy2011
AU  - Elabbasy, E. M.
AU  - Elzeiny, Sh. R.
TI  - Oscillation theorems concerning non-linear differential equations of the second order
ST  - Oscillation theorems concerning non-linear differential equations of the second order
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2011
VL  - 31
IS  - 3
SP  - 373
EP  - 391
DO  - http://dx.doi.org/10.7494/OpMath.2011.31.3.373
UR  - http://dx.doi.org/10.7494/OpMath.2011.31.3.373
AB  - This paper concerns the oscillation of solutions of the differential eq. \[ \left[ r\left( t\right) \psi \left(x\left( t\right) \right) f\text{ }( \overset{\cdot }{x}(t))\right]^{\cdot }+q\left( t\right) \varphi (g\left( x\left( t\right) \right), r\left( t\right) \psi \left( x\left( t\right) \right) f(\overset{\cdot }{x}(t)))=0,\] where \(u\varphi \left( u,v\right) \gt 0\) for all \(u\neq 0\), \(xg\left( x\right) \gt 0\), \(xf\left( x\right)\gt 0\) for all \(x\neq 0\), \(\psi \left( x\right) \gt 0\) for all \(x\in \mathbb{R}\), \(r\left( t\right) \gt 0\) for \(t\geq t_{0}\gt 0\) and \(q\) is of arbitrary sign. Our results complement the results in [A.G. Kartsatos, On oscillation of nonlinear equations of second order, J. Math. Anal. Appl. 24 (1968), 665–668], and improve a number of existing oscillation criteria. Our main results are illustrated with examples.
KW  - second order
KW  - nonlinear
KW  - differential equations
KW  - oscillation
SN  - 1232-9274
ER  -