The Cauchy–nicoletti Problem with Poles
نویسنده
چکیده
The Cauchy–Nicoletti boundary value problem for a system of ordinary differential equations with pole-type singularities is investigated. The conditions of the existence, uniqueness, and nonuniqueness of a solution in the class of continuously differentiable functions are given. The classical Banach contraction principle is combined with a special transformation of the original problem. Introduction This paper deals with the Cauchy–Nicoletti problem for a system of differential equations with poles, i.e., with the problem (t− ai)ixi =
منابع مشابه
Nonuniqueness Theorem for a Singular Cauchy-nicoletti Problem
The nonuniqueness of a regular or singular Cauchy problem for ordinary differential equations is studied in several papers such as [3, 4, 5, 13, 14, 15, 16, 17]. Most of these results can also be found in the monograph [1]. The uniqueness of solutions of Cauchy initial value problem for ordinary differential equations with singularity is investigated in [7, 8, 9, 12]. The topological structure ...
متن کاملA Multidimensional Singular Boundary Value Problem of the Cauchy–nicoletti Type
A two-point singular boundary value problem of the Cauchy–Nicoletti type is studied by introducing a two-point boundary value set and using the topological principle. The results on the existence of solutions whose graph lies in this set are proved. Applications and comparisons to the known results are given, too. Introduction Consider the system of ordinary differential equations y′ = f(x, y),...
متن کاملThree-point Singular Boundary-value Problem for a System of Three Differential Equations *
A singular Cauchy-Nicoletti problem for a system of three ordinary differential equations is considered. An approach which combines topological method of T. Ważewski and Schauder’s principle is used. Theorem concerning the existence of a solution of this problem (a graph of which lies in a given domain) is proved. Moreover, an estimation of its coordinates is obtained.
متن کاملNvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition
Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...
متن کاملExistence of Mild Solutions to a Cauchy Problem Presented by Fractional Evolution Equation with an Integral Initial Condition
In this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional Cauchy problem with an integral initial condition in Banach spaces.
متن کامل