Oscillation of second order superlinear dynamic equations with damping on time scales

This paper concerns the oscillation of solutions to the second order superlinear dynamic equation with damping (r(t)x^@D(t))^@D+p(t)x^@D(t)+q(t)f(x^@s(t))=0, on a time scale T which is unbounded above. No sign conditions are imposed on r(t), p(t) and q(t). The function f@?C(R,R) is assumed to satisfy xf(x)>0 and f^'(x)>0, for x 0. We illustrate the results by several examples.

[1]  A. Peterson,et al.  Difference Equations: An Introduction with Applications , 2000 .

[2]  Samir H. Saker,et al.  Oscillation Criteria for Half-Linear Delay Dynamic Equations on Time Scales , 2009 .

[3]  W. T. Patula,et al.  A second-order nonlinear difference equation: Oscillation and asymptotic behavior , 1983 .

[4]  A. Peterson,et al.  Boundedness and oscillation for nonlinear dynamic equations on a time scale , 2003 .

[5]  William Benjamin Fite,et al.  Concerning the zeros of the solutions of certain differential equations , 1918 .

[6]  Elmetwally M. Elabbasy,et al.  Oscillation of second-order nonlinear differential equations with damping term , 2007 .

[7]  Lynn Erbe,et al.  Oscillation criteria for nonlinear functional neutral dynamic equations on time scales , 2009 .

[8]  A. Peterson,et al.  Advances in Dynamic Equations on Time Scales , 2012 .

[9]  Lynn Erbe,et al.  Oscillation criteria for nonlinear damped dynamic equations on time scales , 2008, Appl. Math. Comput..

[10]  Lynn Erbe,et al.  Oscillation Results for Second-order Linear Equations on a Time Scale , 2002 .

[11]  Samir H. Saker,et al.  Oscillation Criteria for Sublinear Half-Linear Delay Dynamic Equations , 2009 .

[12]  E. Elabbasy,et al.  Interval oscillation for second order sublinear differential equations with a damping term , 2008 .

[13]  A. Peterson,et al.  Kiguradze-type Oscillation Theorems for Second Order Superlinear Dynamic Equations on Time Scales , 2011, Canadian Mathematical Bulletin.

[14]  J. Wong.  Oscillation criteria for second order nonlinear differential equations involving general means , 2000 .

[15]  F. V. Atkinson,et al.  On second-order non-linear oscillations , 1955 .

[16]  Martin Bohner,et al.  Oscillation for Nonlinear Second Order Dynamic Equations on a Time Scale , 2005 .

[17]  A. Peterson,et al.  Dynamic Equations on Time Scales: An Introduction with Applications , 2001 .

[18]  Aurel Wintner,et al.  A criterion of oscillatory stability , 1949 .

[19]  Taher S. Hassan,et al.  Oscillation criteria for half-linear dynamic equations on time scales , 2008 .