The Journal of the Indian Mathematical Society

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Bounded Oscillation and Convergence of Solutions in a Neutral Differential Equation with Oscillating Coefficients


Affiliations
1 Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Dist-Sambalpur, 768018, Orissa, India
2 Department of Mathematics, Silicon Institute of Technology, Bhubaneswar, Orissa, India
3 Department of Computer Science, K.I.S.T, Bhubaneswar, Orissa, India
     

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In this paper sufficient conditions are obtained so that every bounded solution of

(y(t)-p(t)y(t-τ))' + Q(t)G(y(t-σ)) = f(t)

oscillates or tends to zero as t→1, where the coefficient functions Q(t), and f(t) are assumed to be oscillatory. It is known that such assumptions on coefficient functions are very rare in literature. Different ranges for p(t) are considered including the case when p(t) changes sign. The results hold for all types of the non-linear function G and also hold when f(t)≡0.


Keywords

Oscillatory Solution, Non Oscillatory Solution, Asymptotic Behaviour.
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  • Bounded Oscillation and Convergence of Solutions in a Neutral Differential Equation with Oscillating Coefficients

Abstract Views: 233  |  PDF Views: 0

Authors

R. N. Rath
Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Dist-Sambalpur, 768018, Orissa, India
P. P. Mishra
Department of Mathematics, Silicon Institute of Technology, Bhubaneswar, Orissa, India
L. N. Padhy
Department of Computer Science, K.I.S.T, Bhubaneswar, Orissa, India

Abstract


In this paper sufficient conditions are obtained so that every bounded solution of

(y(t)-p(t)y(t-τ))' + Q(t)G(y(t-σ)) = f(t)

oscillates or tends to zero as t→1, where the coefficient functions Q(t), and f(t) are assumed to be oscillatory. It is known that such assumptions on coefficient functions are very rare in literature. Different ranges for p(t) are considered including the case when p(t) changes sign. The results hold for all types of the non-linear function G and also hold when f(t)≡0.


Keywords


Oscillatory Solution, Non Oscillatory Solution, Asymptotic Behaviour.