Related papers: Solutions and Green's function of the first order …
Using Gegenbauer polynomials and the zonal harmonic functions we build an explicit representation formula for the Green function with Neumann boundary conditions in the annulus.
In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…
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…
Stieltjes boundary problems generalize the customary class of well-posed two-point boundary value problems in three independent directions, regarding the specification of the boundary conditions: (1) They allow more than two evaluation…
A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained.
In this paper, we study the Cauchy problem of a higher-order $\mu$-Camassa-Holm equation. We first establish the Green's function of $(\mu-\partial_{x}^{2}+\partial_{x}^{4})^{-1}$ and local well-posedness for the equation in Sobolev spaces…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
The behavior of solutions to the biharmonic equation is well-understood in smooth domains. In the past two decades substantial progress has also been made for the polyhedral domains and domains with Lipschitz boundaries. However, very…
By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second…
In this paper we introduce a common problem in electronic measurements and electrical engineering: finding the first root from the left of an equation in the presence of some initial conditions. We present examples of electrotechnical…
A new expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is…
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…
We study first order linear partial differential equations that appear, for example, in the analysis of dimishing urn models with the help of the method of characteristics and formulate sufficient conditions for a central limit theorem.
We study counter-terms of one- and two-point Green functions of some special operators in ${\cal N}=1$ SYM from their SUGRA duals from the consideration of AdS/CFT or gauge/gravity correspondence. We consider both the Maldacena-Nunez…
Various Green functions of the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov-Bohm field and a collinear uniform magnetic field) are constructed and studied. The problem is considered in 2+1 and 3+1…
A Green's function method is developed for solving strongly-coupled gravity and matter in the semiclassical limit. In the strong-coupling limit, one assumes that Newton's constant approaches infinity. As a result, one may neglect second…
The main point of this paper is to present a class of equations over integers that one can check if they have a solution by checking a set of inequalities. The prototype of such equations is the equations appearing in the well-known…
We consider a general one-particle Hamiltonian H = - \Delta_r + u(r) defined in a d-dimensional domain. The object of interest is the time-independent Green function G_z(r,r') = < r | (z-H)^{-1} | r' >. Recently, in one dimension (1D), the…
We propose two ways for determining the Green's matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form on some basis representation. In addition to the recurrence relation comming from…