Related papers: Basic theory of a class of linear functional diffe…
Szalai et al. (SIAM J. on Sci. Comp. 28(4), 2006) gave a general construction for characteristic matrices for systems of linear delay-differential equations with periodic coefficients. First, we show that matrices constructed in this way…
We study the linear Pfaffian systems satisfied by a certain class of hypergeometric functions, which includes Gau\ss's ${}_2 F_{1}$, Thomae's ${}_L F_{L-1}$ and Appell-Lauricella's $F_D$. In particular, we present a fundamental system of…
We study function-valued solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable parabolicity hypotheses. We provide…
The so-called polynomial equations play an important role both in algebra and in the theory of functional equations. If the unknown functions in the equation are additive, relatively many results are known. However, even in this case, there…
Many theorems of mathematics have the form that for a certain problem, e.g. a differential equation or polynomial (in)equality, there exists a solution. The sequential version then states that for a sequence of problems, there is a sequence…
The first aim of this work is to establish a Peano type existence theorem for an initial value problem involving complex fractional derivative and the second is, as a consequence of this theorem, to give a partial answer to the local…
The qualitative analysis of the initial value problem P related to a non linear third order parabolic equation typical of diffusive models is discussed. Some basic properties of the the fundamental solution of a related linear operator are…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…
In this study, a collocation method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. Some illustrative examples are given to verify the efficiency and…
We describe a seemingly unnoticed feature of the text-book Maxwell-Lorentz system of classical electrodynamics which challenges its formulation in terms of an initial value problem. For point-charges, even after appropriate renormalization,…
We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-*…
Classes of kinetic differential equations are delineated which do have a quadratic first integral, and classes which can not have one. Example reactions corresponding to the obtained kinetic differential equations are shown, and a few…
In this paper, we study initial value problems for a class of functional equations. We introduce the concept of appropriate initial sets to enable the unique extension of an initial function into a solution defined over larger domains. Our…
The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients. These fundamental solutions are directly connected with multiple…
We discuss initial value problems for time evolution equations in one dimensional space which are expressed by the lattice operators and propose some new equations to which complexity of solutions is of polynomial class. Novel type of…
In this paper, we investigate how the initial models and the final models for the polynomial functors can be uniformly specified in matching logic.
Formulas for the solutions of initial value problems for ordinary differential equations with singular $\delta^{(n)}$-like driving terms are derived in the framework of an algebra of generalized functions (of Colombeau type) over a field of…
In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…