• Kyungpook Mathematical Journal
• /
• 제59권1호
• /
• pp.73-82
• /
• 2019

In this work, we give necessary and sufficient conditions under which every solution of a class of first-order neutral differential equations of the form $$(x(t)+p(t)x({\tau}(t)))^{\prime}+q(t)Hx({\sigma}(t)))=0$$ either oscillates or converges to zero as $t{\rightarrow}{\infty}$ for various ranges of the neutral coefficient p. Our main tools are the Knaster-Tarski fixed point theorem and the Banach's contraction mapping principle.

• Journal of Applied and Pure Mathematics
• /
• 제4권3_4호
• /
• pp.107-122
• /
• 2022

This manuscript aims to investigate the existence, uniqueness, and stability of non-local random impulsive neutral stochastic differential time delay equations (NRINSDEs) with Poisson jumps. First, we prove the existence of mild solutions to this equation using the Banach fixed point theorem. Next, we demonstrate the stability via continuous dependence initial value. Our study extends the work of Wang, and Wu [16] where the time delay is addressed by the prescribed phase space 𝓑 (defined in Section 3). To illustrate the theory, we also provide an example of our methods. Using our results, one could investigate the controllability of random impulsive neutral stochastic differential equations with finite/infinite states. Moreover, one could extend this study to analyze the controllability of fractional-order of NRINSDEs with Poisson jumps as well.

• 충청수학회지
• /
• 제27권1호
• /
• pp.89-97
• /
• 2014

We study the existence of mild solutions for neutral differential equations with nonlocal conditions in the ${\alpha}$-norm.

• 대한수학회보
• /
• 제45권2호
• /
• pp.299-312
• /
• 2008

In this paper, we establish some oscillation criteria for nonautonomous second order neutral delay dynamic equations $(x(t){\pm}r(t)x({\tau}(t)))^{{\Delta}{\Delta}}+H(t,\;x(h_1(t)),\;x^{\Delta}(h_2(t)))=0$ on a time scale ${\mathbb{T}}$. Oscillatory behavior of such equations is not studied before. This is a first paper concerning these equations. The results are not only can be applied on neutral differential equations when ${\mathbb{T}}={\mathbb{R}}$, neutral delay difference equations when ${\mathbb{T}}={\mathbb{N}}$ and for neutral delay q-difference equations when ${\mathbb{T}}=q^{\mathbb{N}}$ for q>1, but also improved most previous results. Finally, we give some examples to illustrate our main results. These examples arc [lot discussed before and there is no previous theorems determine the oscillatory behavior of such equations.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제16권2호
• /
• pp.93-105
• /
• 2012

In this paper, we consider the controllability of a certain class of impulsive neutral evolution differential equations in Banach spaces. Sufficient conditions for controllability are obtained by using the Hausdorff measure of noncompactness and Monch fixed point theorem under the assumption of noncompactness of the evolution system.

• 대한수학회지
• /
• 제53권5호
• /
• pp.1019-1036
• /
• 2016

In this paper, we study the existence of solutions and $L^2$-regularity for fractional order retarded neutral functional differential equations in Hilbert spaces. We no longer require the compactness of structural operators to prove the existence of continuous solutions of the non-linear differential system, but instead we investigate the relation between the regularity of solutions of fractional order retarded neutral functional differential systems with unbounded principal operators and that of its corresponding linear system excluded by the nonlinear term. Finally, we give a simple example to which our main result can be applied.

• Kyungpook Mathematical Journal
• /
• 제47권1호
• /
• pp.1-20
• /
• 2007

In this paper, oscillation and nonoscillation criteria are established for nonlinear neutral delay differential equations with several positive and negative coefficients $$[x(t)-R(t)x(t-r)]^{\prime}+\sum_{i=1}^{m}Pi(t)H_i(x(t-{\tau}_i))-\sum_{j=1}^{n}Q_j(t)H_j(x(t-{\sigma}_j))=0$$. Our criteria improve and extend many results known in the literature. In addition we prove that under appropriate hypotheses, if every solution of the associated linear equation with constant coefficients, $$y^{\prime}(t)+\sum_{i=1}^{m}(p_i-\sum_{k{\in}J_i}qk)y(t-{\tau}_i)=0$$, oscillates, then every solution of the nonlinear equation also oscillates.

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 2001년도 추계학술대회 학술발표 논문집
• /
• pp.337-340
• /
• 2001

In this paper, we consider the observability conditions for the following nonlinear fuzzy neutral functional differential equations : (equation omitted), where x(t) is state function on E$\_$N/$\^$2/, u(t) is control function on E$\_$N/$\^$2/ and nonlinear continuous functions f:J C$\_$0/ E$\_$N/$\^$2/, k:J C$\_$0/ E$\_$N/$\^$2/ are satisfies global Lipschitz conditions.

• Kyungpook Mathematical Journal
• /
• 제46권2호
• /
• pp.273-284
• /
• 2006

In this paper, we study nonoscillatory solutions of a class of second order nonlinear neutral delay differential equations with positive and negative coefficients. Some sufficient conditions for existence of nonoscillatory solutions are obtained.

• 대한수학회보
• /
• 제45권4호
• /
• pp.663-670
• /
• 2008

In this paper, the aim is to solve the neutral delay differential equations in the following form using multiquadric approximation scheme, (1) $$\{_{\;y(t)\;=\;{\phi}(t),\;\;\;\;\;t\;{\leq}\;{t_1},}^{\;y'(t)\;=\;f(t,\;y(t),\;y(t\;-\;{\tau}(t,\;y(t))),\;y'(t\;-\;{\sigma}(t,\;y(t)))),\;{t_1}\;{\leq}\;t\;{\leq}\;{t_f},}$$ where f : $[t_1,\;t_f]\;{\times}\;R\;{\times}\;R\;{\times}\;R\;{\rightarrow}\;R$ is a smooth function, $\tau(t,\;y(t))$ and $\sigma(t,\;y(t))$ are continuous functions on $[t_1,\;t_f]{\times}R$ such that t-$\tau(t,\;y(t))$ < $t_f$ and t - $\sigma(t,\;y(t))$ < $t_f$. Also $\phi(t)$ represents the initial function or the initial data. Hence, we present the advantage of using the multiquadric approximation scheme. In the sequel, presented numerical solutions of some experiments, illustrate the high accuracy and the efficiency of the proposed method even where the data points are scattered.