Iterative oscillation tests for differential equations with several non-monotone arguments

Sufficient oscillation conditions involving lim sup and lim inf for first-order differential equations with several non-monotone deviating arguments and nonnegative coefficients are obtained. The results are based on the iterative application of the Grönwall inequality. Examples illustrating the significance of the results are also given.

[1]  Ioannis P. Stavroulakis,et al.  Oscillation criteria for delay and difference equations with non-monotone arguments , 2014, Appl. Math. Comput..

[2]  Oscillations of difference equations with several delays , 2002 .

[3]  George E. Chatzarakis,et al.  Oscillations of difference equations with several deviated arguments , 2014 .

[4]  L. Erbe,et al.  Oscillation for first order linear differential equations with deviating arguments , 1988, Differential and Integral Equations.

[5]  L. Ė. Ėlʹsgolʹt︠s︡.  Introduction to the theory of differential equations with deviating arguments , 1966 .

[6]  L. Berezansky,et al.  On Existence of Positive Solutions for Linear Difference Equations with Several Delays , 2006 .

[7]  Xianhua Tang,et al.  Oscillation of first order delay differential equations with distributed delay , 2004 .

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

[9]  C. Tian,et al.  Nonexistence and existence of positive solutions for difference equations with unbounded delay , 1998 .

[10]  L. Berezansky,et al.  Nonoscillation Theory of Functional Differential Equations with Applications , 2012 .

[11]  R. Koplatadze,et al.  On the oscillation of solutions of first-order delay differential inequalities and equations , 1994, Georgian Mathematical Journal.

[12]  Zhiguo Luo,et al.  New Oscillation Criteria for Delay Difference Equations , 2001 .

[13]  Elena Braverman,et al.  On oscillation of differential and difference equations with non-monotone delays , 2011, Appl. Math. Comput..

[14]  J. Yu,et al.  Oscillation of delay difference equations , 1994 .

[15]  朱德明,et al.  OSCILLATION OF ADVANCED DIFFERENCE EQUATIONS WITH VARIABLE COEFFICIENTS , 2002 .

[16]  Xiaoping Wang.  Oscillation of delay difference equations with several delays , 2003 .

[17]  C. F. Li,et al.  Oscillation of a nonlinear difference equation with several delays , 2003 .

[18]  H. Onose.  Oscillatory properties of the first order differential inequalities with deviating argument , 1983 .

[19]  George E. Chatzarakis,et al.  Oscillations of differential equations with several non-monotone advanced arguments , 2015 .

[20]  George E. Chatzarakis,et al.  Oscillation criteria of difference equations with several deviating arguments , 2014 .

[21]  M. Kulenovic,et al.  Some comparison and oscillation results for first-order differential equations and inequalities with a deviating argument , 1988 .

[22]  Takaŝi Kusano,et al.  Oscillation theory of first order functional differential equations with deviating arguments , 1984 .

[23]  Ravi P. Agarwal,et al.  Oscillation of Differential Equations with Deviating Arguments , 2003 .

[24]  Á. Elbert,et al.  OSCILLATIONS OF FIRST ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS , 1992 .

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

[26]  John L. Casti,et al.  Introduction to the theory and application of differential equations with deviating arguments , 1973 .

[27]  V. Lakshmikantham,et al.  Oscillation Theory of Differential Equations With Deviating Arguments , 1987 .

[28]  J. Yorke,et al.  When all solutions of x′ = −∑ qi(t) x(t − Ti(t)) oscillate , 1984 .

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

[30]  Elena Braverman,et al.  On nonoscillation of mixed advanced-delay differential equations with positive and negative coefficients , 2009, Comput. Math. Appl..

[31]  Ferenc A. Bartha,et al.  Local stability implies global stability for the 2-dimensional Ricker map , 2012, 1209.2406.

[32]  L. E. El'sgolt's.  Introduction to the Theory of Differential Equations with Deviating Arguments , 1966 .

[33]  T. Kusano.  On even-order functional differential equations with advanced and retarded arguments , 1982 .