Interval criteria for second-order super-half-linear functional dynamic equations with delay and advance arguments

Interval oscillation criteria are established for second-order forced super half-linear dynamic equations on time scales containing both delay and advance arguments, where the potentials and forcing term are allowed to change sign. Four discrete examples are provided to illustrate the relevance of the results. The theory can be applied to second-order dynamic equations regardless of the choice of delta or nabla derivatives.

[1]  俞元洪.  OSCILLATIONS CAUSED BY SEVERAL RETARDED AND ADVANCED ARGUMENTS , 1990 .

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

[3]  Samir H. Saker,et al.  Hille-Kneser-type criteria for second-order dynamic equations on time scales , 2006 .

[4]  A. Sikorska-Nowak,et al.  Dynamic equations (…) on time scales , 2011 .

[5]  Deming Zhu,et al.  Oscillation and nonoscillation of advanced differential equations with variable coefficients , 2002 .

[6]  A. Skidmore,et al.  Oscillatory behavior of solutions of y″ + p(x)y = f(x) , 1975 .

[7]  Ravi P. Agarwal,et al.  Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations , 2002 .

[8]  R. Jackson.  Inequalities , 2007, Algebra for Parents.

[9]  A. H. Nasr.  Necessary and Sufficient Conditions for the Oscillation of Forced Nonlinear Second Order Differential Equations with Delayed Argument , 1997 .

[10]  A. Zafer,et al.  Interval oscillation criteria for second order super‐half linear functional differential equations with delay and advanced arguments , 2009 .

[11]  M. A. El-Sayed,et al.  An oscillation criterion for forced second order linear di erential equation , 1993 .

[12]  Agacik Zafer,et al.  Second-order oscillation of forced functional differential equations with oscillatory potentials , 2006, Comput. Math. Appl..

[13]  Qi-Gui Yang,et al.  Interval criteria for oscillation of second-order half-linear differential equations☆ , 2004 .

[14]  G. Ladas,et al.  Oscillation Theory of Delay Differential Equations: With Applications , 1992 .

[15]  Wan-Tong Li,et al.  Interval oscillation of second-order half-linear functional differential equations , 2004, Appl. Math. Comput..

[16]  Douglas R. Anderson,et al.  Oscillation of second-order forced functional dynamic equations with oscillatory potentials , 2007 .

[17]  Yuan Gong Sun.  A note on Nasr's and Wong's papers , 2003 .

[18]  Á. Elbert,et al.  A half-linear second order differential equation , 1979 .

[19]  Pavel Řehák,et al.  Half-linear dynamic equations on time scales: IVP and oscillatory properties , 2002 .

[20]  J. Wong,et al.  Oscillation Criteria for a Forced Second-Order Linear Differential Equation , 1999 .

[21]  Ondřej Došlý,et al.  Half-linear dynamic equations with mixed derivatives. , 2005 .

[22]  Shurong Sun,et al.  Oscillation criteria for second-order half-linear dynamic equations on time scales , 2010 .

[23]  A. H. Nasr.  Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential , 1998 .

[24]  P. Řehák.  Comparison Theorems and Strong Oscillation in the Half-Linear Discrete Oscillation Theory , 2003 .

[25]  John R. Graef,et al.  Oscillation and comparison theorems for half-linear second-order difference equations , 2001 .

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

[27]  S. H. Saker,et al.  Kamenev-type Oscillation Criteria for Second-Order Linear Delay Dynamic Equations , 2007 .

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

[29]  J. D Mirzov,et al.  On some analogs of Sturm's and Kneser's theorems for nonlinear systems , 1976 .

[30]  Samir H. Saker,et al.  Oscillation criteria for second-order nonlinear delay dynamic equations , 2007 .

[31]  P. Řehák.  On certain comparison theorems for half-linear dynamic equations on time scales , 2004 .

[32]  Devrim Çakmak,et al.  Oscillation criteria for certain forced second-order nonlinear differential equations with delayed argument , 2005 .

[33]  Pavel Řehák,et al.  Hardy inequality on time scales and its application to half-linear dynamic equations , 2005 .

[34]  Yu Yuanhong.  Oscillations caused by several retarded and advanced arguments , 1990 .

[35]  Wan-Tong Li,et al.  An oscillation criterion for nonhomogeneous half-linear differential equations , 2002, Appl. Math. Lett..

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

[37]  Qingkai Kong,et al.  Oscillation Theory for Functional Di erential Equations , 1994 .

[38]  Ondřej Došlý,et al.  Half-linear differential equations , 2005 .

[39]  J. V. Manojlovi,et al.  Oscillation criteria for second-order half-linear differential equations , 1999 .

[40]  J. Graef,et al.  Forced oscillation of second order linear and half-linear difference equations , 2002 .