Related papers: On higher index differential-algebraic equations i…
An initial-boundary value problem for a subdiffusion equation with an elliptic operator $A(D)$ in $\mathbb{R}^N$ is considered. The existence and uniqueness theorems for a solution of this problem are proved by the Fourier method.…
In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional…
We show that if $u$ is a solution to a linear elliptic differential equation of order $2m\geq 2$ in the half-space with $t$-independent coefficients, and if $u$ satisfies certain area integral estimates, then the Dirichlet and Neumann…
We formulate a conjecture classifying algebraic solutions to (possibly non-linear) algebraic differential equations, in terms of the primes appearing in the denominators of the coefficients of their Taylor expansion at a non-singular point.…
In this paper we consider a boundary value problem for fully fourth order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation…
In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…
We consider initial/boundary value problems for time-fractional parabolic PDE of order $0<\alpha<1$ with Caputo fractional derivative (also called fractional diffusion equations in the literature). We prove well-posedness of corresponding…
We obtain a maximum principle, and "a priori" upper estimates for solutions of a class of non linear singular elliptic differential inequalities on Riemannian manifolds under the sole geometrical assumption of volume growth conditions.…
This is the first of a series of papers devoted to the study of classical initial-boundary value problems of Dirichlet, Neumann and mixed type for the Nonlinear Schr\"odinger equation on the segment. Considering proper periodic…
Given finitely many consecutive terms of an infinite sequence, we discuss the construction of a polynomial difference equation that the sequence may satisfy. We also present a method to seek a candidate polynomial differential equation for…
An initial-boundary value problem with homogeneous Dirichlet boundary conditions for three-dimensional Zakharov-Kuznetsov equation is considered. Results on global existence, uniqueness and large-time decay of weak solutions in certain…
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…
For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior…
We are concerned with the arithmetic of solutions to ordinary or partial nonlinear differential equations which are algebraic in the indeterminates and their derivatives. We call these solutions D-algebraic functions, and their equations…
In the article, in a rectangular domain, by the Fourier method, the initial boundary value problem for a high-order equation with two lines of degeneracy with a fractional derivative in the sense of Caputo is investigated for uniqueness and…
In this paper, we first prove the existence of solutions to Dirichlet problems involving the fractional $g$-Laplacian operator and lower order terms by appealing to sub- and supersolution methods. Moreover, we also state the existence of…
We study the solvability of the second boundary value problem of a class of highly singular, fully nonlinear fourth order equations of Abreu type in higher dimensions under either a smallness condition or radial symmetry.
We study fractional differential equations of Riemann-Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on $\mathbb{R}$, we define fractional operators by means of a functional calculus…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
Given a linear ordinary differential equation (ODE) on $\RE$ and a set of interface conditions at a finite set of points $I \subset \RE$, we consider the problem of determining another differential equation whose {\it global} solutions…