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1

On the qualitative behavior of the solutions to second-order neutral delay differential equations

Chatzarakis George E., Santra Shyam S.

Fasciculi Mathematici

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2020

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nr 64

43--56

EN

In this paper, we study the qualitative behavior of the solutions to second-order neutral delay differential equations of the form (r(t) ((x(t) + p(t)x(τ (t)))′)γ)′ + q(t)f (x(σ(t))) = 0. Our main tool is Lebesgue’s dominated convergence theorem. Examples illustrating the applicability of the results are also given.

2

Oscillation results for higher order nonlinear neutral differential equations with positive and negative coefficients

Panigrahi S, Basu R.

Journal of Applied Analysis

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2015

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Vol. 21, nr 2

109--121

EN

In this paper, the authors investigated oscillatory and asymptotic behavior of solutions of a class of nonlinear higher order neutral differential equations with positive and negative coefficients. The results in this paper generalize the results of Tripathy, Panigrahi and Basu [5]. We establish new conditions which guarantees that every solution either oscillatory or converges to zero. Moreover, using the Banach Fixed Point Theorem sufficient conditions are obtained for the existence of bounded positive solutions. Examples are considered to illustrate the main results.

3

On existence of solutions of impulsive nonlinear functional neutral integro-differential equations with nonlocal condition

Jain R. S., Dhakne M. B.

Demonstratio Mathematica

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2015

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Vol. 48, nr 3

413--423

EN

In the present paper, we investigate the existence, uniqueness and continuous dependence of mild solutions of an impulsive neutral integro-differential equations with nonlocal condition in Banach spaces. We use Banach contraction principle and the theory of fractional power of operators to obtain our results.

4

On the existence of positive periodic solutions for totally nonlinear neutral differential equations of the second-order with functional delay

Essel E. K., Yankson E.

Opuscula Mathematica

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2014

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Vol. 34, no. 3

469--481

EN

We prove that the totally nonlinear second-order neutral differential equation [formula] has positive periodic solutions by employing the Krasnoselskii-Burton hybrid fixed point theorem.

5

Oscillatory and asymptotic behavior of fourth order nonlinear neutral delay differential equations with positive and negative coefficients

Tripathy A. K., Panigrahi S, Basu R

Fasciculi Mathematici

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2014

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Nr 52

155--174

EN

In this paper, Oscillatory and asymptotic behaviour of solutions of a class of nonlinear fourth order neutral differential equations with positive and negative coefficients of the form (H) (r(t)(y(t) + p(t)y(t - τ))")" + q(t)G(y(t - α)) - h(t) H (y(t - β)) = 0 and (NH) (H) (r(t)(y(t) + p(t)y(t - τ))")" + q(t)G(y(t - α)) - h(t) H (y(t - β)) =f (t) are studied under the assumption ...[wzór] for various ranges of p(t). Using Schauder’s fixed point theorem, sufficient conditions are obtained for the existence of bounded positive solutions of (NH).