Results 261 to 270 of about 89,989 (306)

Linear functional differential equations with Property A

Journal of Mathematical Analysis and Applications, 2003
The paper deals with oscillatory properties of the linear functional- differential equation \[ u^{(n)}(t)+ \sum^m_{i=1} \int^{\sigma_i(t)}_{\tau_i(t)} u(s)\,d_s r_i(s, t)= 0, \] where \(n\geq 2\), \(\tau_i(t)\leq \sigma_i(t)\), \(\tau_i(t)\to \infty\) for \(t\to\infty\) and the functions \(r_i\) are nondecreasing in the first argument and Lebesgue ...
Grammatikopulos, M.K., Koplatadze, R., Kvinikadze, G.   +2 more
exaly   +3 more sources

Hyers–Ulam stability of linear functional differential equations

Journal of Mathematical Analysis and Applications, 2015
Dealing with delay differential equations of the form \[ y^{(n)}(t)=g(t)\,y(t-\tau)+h(t)\text{ \;on \;}[0,b] \] where \(\tau>0\), the notion of Hyers-Ulan stability is first introduced and then investigated via different methods. Popular approachs, such as, iteraction method and fixed point method, are used to obtain the stability results.
Jinghao Huang, Yongjin Li
exaly   +3 more sources

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Controlling linear functional differential equation

Applicable Analysis, 2001
Necessary conditions for the optimal control of a linear system of neutral type functional differential equations are obtained. We show that a success in reducing the initial problem to the problem of solvability of a certain boundary value problem is, in principle, a question of one's ability to construct adjoint operators to the operators appearing ...
Michael Drakhlin, Elena Litsyn
openaire   +1 more source

On Bounded Solutions of Systems of Linear Functional Differential Equations

Georgian Mathematical Journal, 1999
Abstract Sufficient conditions of the existence and uniqueness of bounded on real axis solutions of systems of linear functional differential equations are established.
Robert Hakl
exaly   +3 more sources

Linear functional-differential equations on the line

Nonlinear Analysis: Theory, Methods & Applications, 1997
The multidimensional equation \(\sum_{j=1}^{l}(D_jy)(F_jx)=\gamma (x)\) is considered. Here \(x \in {\mathbb{R}^1}\) and \(D_j:C^{\infty }({\mathbb{R}^1}, C^m) \to C^{\infty }({\mathbb{R}^1}, C^m)\) are given linear differential operators. A theory of this equation via ``common dynamics'' of the maps \(F_j\) is built.
Belitskii, G. R., Nicolaevsky, Victor M.
openaire   +2 more sources

On Equivalence of Linear Functional-Differential Equations

Results in Mathematics, 1994
The first order ordinary differential equations \(y'(x) = p_0 (x)y(x) + \sum ^k_{i = 1} p_i (x)y (\psi_i (x))\) (with \(k\) deviating arguments, \(k \geq 1\) is fixed) are divided into equivalence classes by means of transformations \(x = h(t)\) and \(z(t) = f(t) y(h(t))\). The author deals with the classes that contains an equation with \(k\) constant
openaire   +1 more source

Linear Functional Differential Equations as Semigroups on Product Spaces

SIAM Journal on Mathematical Analysis, 1983
In this paper we consider the well-posedness of linear functional differential equations on product spaces. Let L and D be linear $\mathbb{R}^n $-valued functions with domains $\mathfrak{D}(L)$ and $\mathfrak{D}(D)$ subspaces of the Lebesgue measurable $\mathbb{R}^n $-valued functions on $[ - r,0]$ and such that $W^{1,p} ([ - r,0];\mathbb{R}^n ...
Burns, John A., Herdman, Terry L., Stech, Harlan W.   +2 more
openaire   +2 more sources