OSCILLATION AND BOUNDEDNESS OF SOLUTIONS TO FIRST AND SECOND ORDER FORCED FUNCTIONAL DYNAMIC EQUATIONS WITH MIXED NONLINEARITIES

We investigate the oscillation and boundedness of first and second order dynamic equations with mixed nonlinearities. Our results extend and improve known results for oscillation of first and second order dynamic equations that have been established by Agarwal and Bohner. Some examples are given to illustrate the main results.

[1]  Liao Mei-li Forced Oscillation of Second-Order Functional Differential Equations , 2006 .

[2]  L. Erbe,et al.  Oscillation Criteria for Forced Second-Order Functional Dynamic Equations with Mixed Nonlinearities on Time Scales , 2010 .

[3]  Taher S. Hassan,et al.  Oscillation of third order nonlinear delay dynamic equations on time scales , 2009, Math. Comput. Model..

[4]  Ravi P. Agarwal,et al.  Oscillation of Second Order Delay Dynamic Equations , 2005 .

[5]  Martin Bohner,et al.  Oscillation and nonoscillation of forced second order dynamic equations , 2007 .

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

[7]  S. Hilger Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus , 1990 .

[8]  Wan-Tong Li,et al.  Nonoscillation and Oscillation Theory for Functional Differential Equations , 2004 .

[9]  M. Bohner,et al.  On the oscillation of second-order half-linear dynamic equations 1 , 2009 .

[10]  Ravi P. Agarwal,et al.  On the oscillation of second-order half-linear dynamic equations1 , 2009 .

[11]  Martin Bohner,et al.  Oscillation of Second Order Nonlinear Dynamic Equations on Time Scales , 2004 .

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

[13]  A. Peterson,et al.  Applicable Analysis and Discrete Mathematics Oscillation Criteria for First Order Forced Dynamic Equations , 2022 .

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

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

[16]  Samir H. Saker,et al.  Oscillation Criteria for Second‐Order Nonlinear Dynamic Equations On Time Scales , 2003 .

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

[18]  Ravi P. Agarwal,et al.  Discrete Oscillation Theory , 2005 .

[19]  Lynn Erbe,et al.  Oscillation of third order nonlinear functional dynamic equations on time scales , 2010 .

[20]  Ravi P. Agarwal,et al.  Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations , 2009 .

[21]  M. Bohner,et al.  Oscillation and Boundedness of Solutions to First and Second Order Forced Dynamic Equations with Mixed Nonlinearities , 2008 .

[22]  Ravi P. Agarwal,et al.  Oscillation criteria for first and second order forced difference equations with mixed nonlinearities , 2007, Math. Comput. Model..

[23]  Ravi P. Agarwal,et al.  Oscillation Theory for Difference and Functional Differential Equations , 2000 .

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

[25]  Martin Bohner,et al.  Oscillation criteria for perturbed nonlinear dynamic equations , 2004, Math. Comput. Model..