Boundary value problem solution existence for linear integro-differential equations with many delays
Journal Title: Карпатські математичні публікації - Year 2018, Vol 10, Issue 1
Abstract
For the study of boundary value problems for delay differential equations, the contraction mapping principle and topological methods are used to obtain sufficient conditions for the existence of a solution of differential equations with a constant delay. In this paper, the ideas of the contraction mapping principle are used to obtain sufficient conditions for the existence of a solution of linear boundary value problems for integro-differential equations with many variable delays. Smoothness properties of the solutions of such equations are studied and the definition of the boundary value problem solution is proposed. Properties of the variable delays are analyzed and functional space is obtained in which the boundary value problem is equivalent to a special integral equation. Sufficient, simple for practical verification coefficient conditions for the original equation are found under which there exists a unique solution of the boundary value problem.
Authors and Affiliations
I. M. Cherevko, A. B. Dorosh
Pointwise stabilization of the Poisson integral for the diffusion type equations with inertia
In this paper we consider the pointwise stabilization of the Poisson integral for the diffusion type equations with inertia in the case of finite number of parabolic degeneracy groups. We establish necessary and sufficie...
Green-Rvachev's quasi-function method for constructing two-sided approximations to positive solution of nonlinear boundary value problems
A homogeneous Dirichlet problem for a semilinear elliptic equations with the Laplace operator and Helmholtz operator is investigated. To construct the two-sided approximations to a positive solution of this boundary valu...
Operators of stochastic differentiation on spaces of nonregular generalized functions of Levy white noise analysis
The operators of stochastic differentiation, which are closely related with the extended Skorohod stochastic integral and with the Hida stochastic derivative, play an important role in the classical (Gaussian) white nois...
Metric on the spectrum of the algebra of entire symmetric functions of bounded type on the complex $L_\infty$
It is known that every complex-valued homomorphism of the Fr\'{e}chet algebra $H_{bs}(L_\infty)$ of all entire symmetric functions of bounded type on the complex Banach space $L_\infty$ is a point-evaluation functional...
Advancement on the study of growth analysis of differential polynomial and differential monomial in the light of slowly increasing functions
Study of the growth analysis of entire or meromorphic functions has generally been done through their Nevanlinna's characteristic function in comparison with those of exponential function. But if one is interested to com...