EXISTENCE OF NONOSCILLATORY SOLUTIONS OF SECOND-ORDER NEUTRAL DIFFERENTIAL EQUATIONS

Year 2019, Volume: 9 Issue: 3, 666 - 674, 01.09.2019

B. Çına T. Candan M. T. Şenel

Abstract

We obtain some sucient conditions for the existence of nonoscillatory solutions of nonlinear second order neutral dierential equation with forcing term. Our results improve and extend some existing results. Examples are also included to illustrate our results.

Keywords

Fixed point, Second-order, Nonoscillatory solution.

References

• Agarwal, Ravi P., Grace, Said R. and O’Regan, Donal, (2000), Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers.
• Agarwal, Ravi P., Bohner Martin and Li, Wan-Tong, (2004), Nonoscillation and Oscillation: Theory for Functional Differential Equations, Marcel Dekker, Inc., New York.
• Candan, T. and Dahiya, R. S., (2010), Existence of nonoscillatory solutions of first and second order neutral differential equations with distributed deviating arguments, J. Franklin Inst., 347, pp. 1309- 1316.
• Candan, T., (2012), The existence of nonoscillatory solutions of higher order nonlinear neutral equa- tions, Appl. Math. Lett., 25(3), pp. 412-416.
• Candan, T. and Dahiya, R. S., (2013), Existence of nonoscillatory solutions of higher order neutral differential equations with distributed deviating arguments, Math. Slovaca, 63(1), pp. 183-190.
• Candan, T., (2015), Nonoscillatory solutions of higher order differential and delay differential equations with forcing term, Appl. Math. Lett., 39, pp. 67-72.
• Erbe, L. H. and Kong, Q. and Zhang, B. G., (1995), Oscillation Theory for Functional Differential Equations, Marcel Dekker, Inc., New York.
• Gy¨ori, I. and Ladas, G., (1991), Oscillation Theory of Delay Differential Equations With Applications, Clarendon Press, Oxford.
• Tian, Y., Cai, Y. and Li, T., (2015), Existence of nonoscillatory solutions to second-order nonlinear neutral difference equations, J. Nonlinear Sci. Appl., 8, pp. 884-892.
• Yang, A., Zhang, Z. and Ge, W., (2008), Existence of nonoscillatory solutions of second-order nonlinearneutral differential equations, Indian J. Pure Appl. Math., 39(3), pp. 227-235.