相关论文: On a Singular Integrodifferential Equation arising…

Integrals related to the surface area of arbitrary ellipsoids are derived, evaluated, and compared with each other and existing integrals found in the literature. We clarify the literature on the ellipsoid area problem, which dates back to…

We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…

This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.

In this paper, we consider two linear inverse problems for the time-fractional wave equation, assuming that its right-hand side takes the separable form $f(t)h(x)$, where $t \geq 0$ and $x \in \Omega \subset R^N $. The objective is to…

We conjecture that many (maybe all) integrable equations and spin systems in 2+1 dimensions can be obtained from the (2+1)-dimensional Gauss-Mainardi-Codazzi and Gauss-Weingarten equations, respectively. We also show that the…

System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of…

In this thesis we consider the free surface flow due to a submerged source in a channel of finite depth. This problem has been considered previously in the literature, with some disagreement about whether or not a train of waves exist on…

In this article we have studied complex linear homogeneous difference equations where the coefficients are meromorphic functions, having finite iterated p-phi order. We have made some estimations on the growth of its nontrivial solutions.…

We introduce a method to find differential equations for functions which define tables, such that associated billiard systems admit a local first integral. We illustrate this method in three situations: the case of (locally) integrable wire…

We study 2D discrete integrable equations of order 1 with respect to one independent variable and $m$ with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The…

A two-dimensional steady problem of a potential free-surface flow of an ideal incompressible fluid caused by a singular sink is considered. The sink is placed at the horizontal bottom of the fluid layer. With the help of the Levi-Civita…

Differential equations where the graph of some derivative of a function is composed of a finite number of similarity transformations of the graph of the function itself are defined. We call these self-similar differential equations (SSDEs)…

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,…

We present results expressing conditions for the existence of meromorphic first integrals for Pfaff equations of arbitrary codimension, integrable or not, on complex manifolds. These results are in the same vein as previous ones by J-P.…

On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…

A method for calculating the meridian profile of the aspherical surface of a plane-convex lens excluding spherical aberration, without calculating the coefficients of the series, by direct solving the compiled differential equation is…

The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…

This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a…

For semilinear wave equations on Lorentzian manifolds with quadratic derivative non-linear terms, we study the inverse problem of determining the background Lorentzian metric. Under some conditions on the nonlinear term, we show that from…

In this paper we discuss the first order partial differential equations resolved with any derivatives. At first, we transform the first order partial differential equation resolved with respect to a time derivative into a system of linear…