相关论文: On a Singular Integrodifferential Equation arising…

Recently, a new fractional derivative called the conformable fractional derivative is given on based basic limit definition derivative in [4]. Then, the fractional versions of chain rules, exponential functions, Gronwalls inequality,…

The aim of the present paper is to study the existence, uniqueness and some other properties of solutions of a certain partial dynamic integrodifferential equations. The Banach fixed point theorem and certain fundamental inequality with…

We study perturbations of linear differential equations, deriving explicit series solutions, using Dyson-type expansions. We analyze the monodromy of deformed solutions in a number of examples, and relate this to cocycles in a cohomological…

We consider the inverse obstacle scattering problem of determining both the shape and the "equivalent impedance" from far field measurements at a fixed frequency. In this work, the surface impedance is represented by a second order surface…

The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…

We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…

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…

We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…

Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method (ESFEM) for space discretization…

We propose an integral transform, called metamorphism, which allow us to reduce the order of a differential equation. For example, the second order Helmholtz equation is transformed into a first order equation, which can be solved by the…

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…

In this paper, we consider a nonlinear Fuchsian type partial differential equation of the second order in the complex domain. Under a very weak assumption, we show the uniqueness of the solution. The result is applied to the problem of…

By using the method developed in the paper [G.Pantsulaia, G.Giorgadze, On some applications of infinite-dimensional cellular matrices, {\it Georg. Inter. J. Sci. Tech., Nova Science Publishers,} Volume 3, Issue 1 (2011), 107-129], it is…

An implicit solution to the vanishing of the so-called Universal Field Equation, or Bordered Hessian, which dates at least as far back as 1935 \cite{chaundy} is revived, and derived from a much later form of the solution. A linear ansatz…

Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory and have attracted interest recently also…

In this work we study the general system of geodesic equations for the case of a massive particle moving on an arbitrary curved manifold. The investigation is carried out from the symmetry perspective. By exploiting the parametrization…

In this paper, we consider the solvability of a class of nonlinear fourth order integro-differential equations with Navier boundary condition. We first deal with a corresponding linear problem and establish a maximum principle. Using the…

We consider the problem of global in time existence and uniqueness of solutions of the 3-D infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher…

Variable order differential equations with non-integrable singularities are considered on spatial networks. Properties of the spectrum are established, and the solution of the inverse spectral problem is obtained.

In this short note, we present an easy to implement and fast algorithm for the computation of the steady solitary gravity wave solution of the free surface Euler equations in irrotational motion. First, the problem is reformulated in a…