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In this paper we study asymptotic behavior of solutions of second order neutral functional differential equation of the form ${(x (t) + p x (t - τ))}^{''} + f (t, x (t)) = 0 .$ We present conditions under which all nonoscillatory solutions are asymptotic to $a t + b$ as $t \to \infty$ , with $a, b \in R$ . The obtained results extend those that are known for equation $u^{''} + f (t, u) = 0 .$

Asymptotic behavior of solutions of non-linear differential equations with deviating arguments via nonstandard analysis

Haruo Murakami, Shin-ichi Nakagiri, Cheh-Chih Yeh (1983)

Annales Polonici Mathematici

Asymptotic behavior of solutions of nonlinear differential equations and generalized guiding functions.

Avramescu, Cezar (2003)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Asymptotic behavior of solutions of nonlinear functional differential equations.

Jung, Jong Soo, Park, Jong Yeoul, Kang, Hong Jae (1994)

International Journal of Mathematics and Mathematical Sciences

Asymptotic behavior of solutions of some functional differential equations by Schauder's theorem.

Furumochi, Tetsuo (2003)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Asymptotic behavior of solutions of third order delay differential equations

Mariella Cecchi, Zuzana Došlá (1997)

Archivum Mathematicum

We give an equivalence criterion on property A and property B for delay third order linear differential equations. We also give comparison results on properties A and B between linear and nonlinear equations, whereby we only suppose that nonlinearity has superlinear growth near infinity.

Asymptotic behavior of solutions to a class of differential variational inequalities

Nguyen Thi Van Anh, Tran Dinh Ke (2015)

Annales Polonici Mathematici

We address some questions concerning a class of differential variational inequalities with finite delays. The existence of exponential decay solutions and a global attractor for the associated multivalued semiflow is proved.

Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature

Shigetoshi Yazaki (2007)

Kybernetika

Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex:...

Asymptotic behavior of solutions to second-order nonlinear differential equations.

Rogovchenko, Svetlana P., Rogovchenko, Yuri V. (2000)

Portugaliae Mathematica

Asymptotic behavior of solutions to some homogeneous second-order evolution equations of monotone type.

Rouhani, Behzad Djafari, Khatibzadeh, Hadi (2007)

Journal of Inequalities and Applications [electronic only]

Asymptotic behavior of $T$ -periodic solutions of singularly perturbed second-order differential equation

Róbert Vrábeľ (1996)

Mathematica Bohemica

Asymptotic behavior of the solutions to a class of second-order differential systems.

Nenov, Svetoslav Ivanov (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion

Rachid Belfadli (2010)

Annales mathématiques Blaise Pascal

We prove, by means of Malliavin calculus, the convergence in $L^{2}$ of some properly renormalized weighted quadratic variations of bi-fractional Brownian motion (biFBM) with parameters $H$ and $K$ , when $H < 1 / 4$ and $K \in (0, 1]$ .

Asymptotic behaviour and Hopf bifurcation of a three-dimensional nonlinear autonomous system.

Baráková, Lenka (2002)

Georgian Mathematical Journal

Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity

Olaf Klein (2004)

Applications of Mathematics

The asymptotic behaviour for $t \to \infty$ of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress...

Asymptotic behaviour for semilinear damped wave equations on $ℝ^{N}$

Feireisl, Eduard (1994)

Equadiff 8

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