On a Class of Functional Differential Equations Having Slowly Varying Solutions

Construction of measures of noncompactness of $C^k(Omega)$ and $C^k_0$ and their application to functional integral-differential equations

‎In this paper‎, ‎first‎, ‎we investigate the construction of compact sets of $ C^k$ and $ C_0^k$‎ ‎by proving ``$C^k‎, ‎C_0^k-version$‎" ‎of Arzel`{a}-Ascoli theorem‎, ‎and then introduce new measures of noncompactness on these spaces‎. ‎Finally‎, ‎as an application‎, ‎we study the existence of entire solutions for a class of the functional integral-differential equations by using Darbo's fixe...

On slowly growing solutions of linear functional differential systems

We obtain new conditions sufficient for the (unique, under an additional condition) solvability of a system of singular functional differential equations with non-increasing operators. 1. Problem setting and motivation The aim of this note is to establish some general conditions sufficient for the existence and uniqueness of a slowly growing solution of a class of singular linear functional dif...

Numerical Solutions of Special Class of Systems of Non-Linear Volterra Integro-Differential Equations by a Simple High Accuracy Method

ON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *

The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.

Slowly Varying Solutions of a Class of First Order Systems of Nonlinear Differential Equations

We analyze positive solutions of the two-dimensional systems of nonlinear differential equations x′ + p(t)y = 0, y′ + q(t)x = 0, (A) x′ = p(t)y, y′ = q(t)x , (B) in the framework of regular variation and indicate the situation in which system (A) (resp. (B)) possesses decaying solutions (resp. growing solutions) with precise asymptotic behavior as t → ∞.