OSCILLATION THEOREMS FOR NONLINEAR SECOND ORDER DIFFERENCE EQUATIONS WITH A NONLINEAR DAMPING TERM

Authors

  • E. THANDAPANI DepartmentofMathematics,MadrasUniversityP.G.Centre,Salem-636Oll,TamilNadu, INDIA.
  • S. PANDIAN Department of Mathematics, Madras University P. G. Centre, Salem-636Oll, TamilNadu, INDIA

DOI:

https://doi.org/10.5556/j.tkjm.26.1995.4378

Keywords:

Difference equation, Nonlinear damped term, Oscillation

Abstract

Some new sufficient conditions for the oscillation of the nonlinear damped second order difference equations of the form

\[\Delta^2 y_n+p_n\phi(y_n, \Delta y_n)+q_nf(y_{n+1})g(\Delta y_n)=0\]

are given.

References

R. P. Agarwal, Difference Equations and Inequalities, Marcel Dakker, New York, 1992

J. W. Baker, "Oscillation theorems for a second order damped non-linear differential equation," SIAM J. Appl Math., 25 (1973), 37-40.

S. R. Grace and B. S. Lalli, "Oscillatory behavior of nonlinear second order differential equations with deviating arguments," Bull. Inst. Math. Acad. Sinica, 14 (1986), 187-196.

J. W. Hooker and W. T. Patula,''A second order non-linear difference equation: Oscillation and asymptotic behaviour," ]. Math. Appl., 91 (1983), 9-24.

M. R. S. Kulenovic and Budincevic, ' 'Asymptotic Analysis of non-linear second order difference equation," Sti. Univ. /asi, 30 (1984), 39-52.

M. Naito, "Oscillation theorems for a damped non-linear differential equation," Proc. Japan, Acad., 50 (1974), 104-108.

J. Popenda, "Oscillation and non-oscillation theorems for second order difference equations," J. Math. Anal. Suppl., 123 (1987), 34-38.

B. Szmanda, "Oscillation criteria for second order non-linear difference equations," Ann. Poln. Math., 43 (1983), 225-235.

B. Szmanda, "Oscillation theorems for non-linear second order difference equations," J. Math. Anal. Appl., 79 (1981), 90-95.

E. Thandapani, "Oscillation criteria for certain second order difference equations," ZAA, 11 (1992), 425-429.

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Published

1995-03-01

How to Cite

THANDAPANI, E., & PANDIAN, S. (1995). OSCILLATION THEOREMS FOR NONLINEAR SECOND ORDER DIFFERENCE EQUATIONS WITH A NONLINEAR DAMPING TERM. Tamkang Journal of Mathematics, 26(1), 49-58. https://doi.org/10.5556/j.tkjm.26.1995.4378

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Papers