Related papers: Regularization of linear impulsive boundary-value …
We prove new results on the existence of positive solutions for some impulsive differential equation subject to nonlocal boundary conditions. Our boundary conditions involve an affine functional given by a Stieltjes integral. These cover…
In this paper we make a subtle use of tools from operator theory and the Schauder fixed-point theorem to establish the existence of pseudo-almost automorphic solutions to some classes of nonautonomous integro-differential equations with…
Several dynamical systems in fields such as engineering, chemistry, biology, and physics show impulsive behavior by reason of unexpected changes at specific times. These behaviors are described by differential systems under impulse effects.…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…
This paper studies the oscillatory behavior of solutions to linear nonautonomous impulsive differential equations with piecewise constant arguments, including both advanced and delayed cases \[ x'(t) = a(t)x(t) + b(t)x([t-k]), \quad k \in…
In this paper an extension of the spectral Lanczos' tau method to systems of nonlinear integro-differential equations is proposed. This extension includes (i) linearization coefficients of orthogonal polynomials products issued from…
The first step when solving an infinite-dimensional eigenvalue problem is often to discretize it. We show that one must be extremely careful when discretizing nonlinear eigenvalue problems. Using examples, we show that discretization can:…
We report a new analytical method for exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients. The method is based on the definition of jump transfer matrices and their extension…
This article addresses control problems for semilinear impulsive neutral integro-differential equations with memory in a Banach space. It investigates the approximate controllability of linear and semilinear systems and proves the…
This book aims to provide a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. Such a class of equations often arises in analysis, probability theory,…
The main objective of this paper is the construction of the solution of an impulsive stochastic differential equation, subject to control conditions in the pulse-times and give sufficient conditions for them to be random variables with…
We consider an impulse control problem in infinite horizon. To solve this problem, we extend to the infinite horizon case results of double barrier reflected backward stochastic differential equations. The properties of the Snell envelope…
We consider a control system with dynamics which are affine in the (unbounded) derivative of the control $u$. We introduce a notion of generalized solution $x$ on $[0,T]$ for controls $u$ of bounded total variation on $[0,t]$ for every…
We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the solution. A dimensional reduction of the problem is obtained…
This paper uses the resolvent operator technique to investigate second-order non-autonomous neutral integrodifferential equations with impulsive conditions in a Banach space. We study the existence of a mild solution and the system's…
In this work, a new technique has been presented to find approximate solution of linear integro-differential equations. The method is based on modified orthonormal Bernoulli polynomials and an operational matrix thereof. The method converts…
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…
We present new criteria for the existence of oscillatory and nonoscillatory solutions of measure delay differential equations with impulses. We deal with the integral forms of the differential equations using the Perron and the…