Linearized Oscillation Results for Even-Order Neutral Differential Equations [PDF]
Czechoslovak Mathematical Journal, 2001 The paper deals with the even order nonlinear neutral equation \((1)\) \((x(t)-P(t)g(x(t-\tau )))^{(n)}-Q(t)h(x(t-\sigma ))=0,\) with \(P,Q\in C([t_0,\infty ),\mathbb R),\) \(g,h\in C (\mathbb R,\mathbb R),\) \(\tau >0,\) \(\sigma \geq 0\) and \(t_0\in \mathbb R.\) In particular, linearized oscillation results for \((1)\) are obtained also in the cases
Shen, J. H., Yu, J. S.
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Even Order Half-Linear Differential Equations with Regularly Varying Coefficients
Mathematics, 2020 We establish nonoscillation criterion for the even order half-linear differential equation (−1)nfn(t)Φx(n)(n)+∑l=1n(−1)n−lβn−lfn−l(t)Φx(n−l)(n−l)=0, where β0,β1,…,βn−1 are real numbers, n∈N, Φ(s)=sp−1sgns for s∈R, p∈(1,∞) and fn−l is a regularly varying (
Vojtěch Růžička
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Asymptotic Properties of Neutral Differential Equations with Variable Coefficients
Axioms, 2020 The aim of this work is to study oscillatory behavior of solutions for even-order neutral nonlinear differential equations. By using the Riccati substitution, a new oscillation conditions is obtained which insures that all solutions to the studied ...
Omar Bazighifan +2 more
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A New Approach in the Study of Oscillation Criteria of Even-Order Neutral Differential Equations
Mathematics, 2020 Based on the comparison with first-order delay equations, we establish a new oscillation criterion for a class of even-order neutral differential equations. Our new criterion improves a number of existing ones. An illustrative example is provided.
Osama Moaaz +2 more
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Properties of even order linear functional differential equations with deviating arguments of mixed type [PDF]
Opuscula Mathematica, 2022 This paper is concerned with oscillatory behavior of linear functional differential equations of the type \[y^{(n)}(t)=p(t)y(\tau(t))\] with mixed deviating arguments which means that its both delayed and advanced parts are unbounded subset of \((0 ...
Jozef Dzurina
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Oscillation Criteria of Higher-order Neutral Differential Equations with Several Deviating Arguments
Mathematics, 2020 This work is concerned with the oscillatory behavior of solutions of even-order neutral differential equations. By using the technique of Riccati transformation and comparison principles with the second-order differential equations, we obtain a new ...
Osama Moaaz +2 more
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New oscillation theorems for a class of even-order neutral delay differential equations
Advances in Difference Equations, 2021 In this work, we study the oscillatory behavior of even-order neutral delay differential equations υ n ( l ) + b ( l ) u ( η ( l ) ) = 0 $\upsilon ^{n}(l)+b(l)u(\eta (l))=0$ , where l ≥ l 0 $l\geq l_{0}$ , n ≥ 4 $n\geq 4$ is an even integer and υ = u + a
Mona Anis, Osama Moaaz
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On the Large Time Behavior of Solutions of Hamilton-Jacobi Equations Associated with Nonlinear Boundary Conditions [PDF]
, 2012 In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions.
A. Davini +30 more
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Even-order differential equation with continuous delay: nonexistence criteria of Kneser solutions
Advances in Difference Equations, 2021 In this paper, we study even-order DEs where we deduce new conditions for nonexistence Kneser solutions for this type of DEs. Based on the nonexistence criteria of Kneser solutions, we establish the criteria for oscillation that take into account the ...
Ali Muhib +2 more
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Oscillation properties of even-order linear differential equations [PDF]
Transactions of the American Mathematical Society, 1965 is considered for r(x) and p(x) continuous and r(x) > 0, p(x) # 0 on [a, a)). For n = 1, this equation has been the subject of many investigations over a number of years. For n = 2, J. H. Barrett [1]-[3] and W. Leighton and Z. Nehari [7] have recently considered equations of this type. For arbitrary n, similar equations have been investigated by W.
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