Property (a) of the N-th Order Differential Equations with Deviating Argument
نویسنده
چکیده
The equation to be considered is Lny(t) + p(t)y((t)) = 0: The aim of this paper is to derive suucient conditions for property (A) of this equation. In the paper a result of D zurina 2] concerning asymptotic properties of the third order linear diierential equations with delay is extended to an n-th order delay diierential equation. We consider the diierential equation (1) L n y(t) + p(t)y((t)) = 0; where n > 3, L n y(t) = 1 r n (t) 1 r n?1 (t) y(t) r 0 (t) 0 ! 0 ; r i (t), i = 0; 1; ; n are positive and continuous functions on some ray t 0 ; 1), (t) < t is increasing function on t 0 ; 1). The expressions L 0 y(t) = y(t) r 0 (t) called quasi-derivatives will be very helpful in the sequel. We will suppose throughout the paper that Z 1 t0
منابع مشابه
Approximately $n$-order linear differential equations
We prove the generalized Hyers--Ulam stability of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.
متن کاملNonlinear Fuzzy Volterra Integro-differential Equation of N-th Order: Analytic Solution and Existence and Uniqueness of Solution
This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...
متن کاملAn Effective Numerical Technique for Solving Second Order Linear Two-Point Boundary Value Problems with Deviating Argument
Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some n...
متن کاملAnti-Periodic Solutions for a Class of Third-Order Nonlinear Differential Equations with a Deviating Argument
In this paper, we study a class of third-order nonlinear differential equations with a deviating argument and establish some sufficient conditions for the existence and exponential stability of anti-periodic solutions of the equation. These conditions are new and complement to previously known results.
متن کاملAn existence result for n^{th}-order nonlinear fractional differential equations
In this paper, we investigate the existence of solutions of some three-point boundary value problems for n-th order nonlinear fractional differential equations with higher boundary conditions by using a fixed point theorem on cones.
متن کامل