相关论文: Growth of Solutions of Complex Differential Equati…

In this paper, we consider the problem of covering a plane region with unit discs. We present an improved upper bound and the first nontrivial lower bound on the number of discs needed for such a covering, depending on the area and…

We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of a linear evolution equation can be…

In this note we prove an estimate on the level sets of a function with $(p, q)$ growth that depends on the difference quotient of a bounded weak solution to a nonlocal double phase equation. This estimate is related to a self improving…

We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove…

We investigate the rate of growth of the function of n which counts the number of complex irreducible representations of a fixed group of degree less than or equal to n. The emphasis is on linear groups, especially compact real and p-adic…

I begin from a particular field of generalised Puiseux series and investigate a class of nonlinear differential equations in the field. It is appeared that the main part of differential equation determines solvability and positions of…

In this paper we introduce a new concept of atoms on discrete sets to develop an advanced method to find a particular solution for higher-order non-homogeneous Cauchy-Euler equations. The proposed method provides also an approximate…

A "fat slit" is a compact domain in the upper half plane bounded by a curve with endpoints on the real axis and a segment of the real axis between them. We consider conformal maps of the upper half plane to the exterior of a fat slit…

Motivated by map labeling, Funke, Krumpe, and Storandt [IWOCA 2016] introduced the following problem: we are given a sequence of $n$ disks in the plane. Initially, all disks have radius $0$, and they grow at constant, but possibly…

We prove existence and regularity results for weak solutions of non linear elliptic systems with non variational structure satisfying $(p,q)$-growth conditions. In particular we are able to prove higher differentiability results under a…

We define two common $q$-orthogonal polynomials: homogeneous $q$-Laguerre polynomials and homogeneous little $q$-Jacobi polynomials. They can be viewed separately as solutions to two $q$-partial differential equations. Then, we proved that…

We study the existence of positive increasing radial solutions for superlinear Neumann problems in the ball. We do not impose any growth condition on the nonlinearity at infinity and our assumptions allow for interactions with the spectrum.…

We present in this paper a detailed note on the computation of Puiseux series solutions of the Riccatti equation associated with a homogeneous linear ordinary differential equation. This paper is a continuation of [1] which was on the…

In this article, we study the growth of meromorphic solutions of linear delay-differential equation of the form \begin{equation*} \sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}(z)f^{(j)}(z+c_{i})=F(z), \end{equation*}% where $A_{ij}(z)$ $(i=0,1,\ldots…

\texttt{DiscoTEX} is a highly accurate numerical algorithm for computing numerical weak-form solutions to distributionally sourced partial differential equations (PDE)s. The aim of this second paper, succeeding \cite{da2024discotex}, is to…

In this paper we are concerned with the regularity of solutions to a nonlinear elliptic system of $m$ equations in divergence form, satisfying $p$ growth from below and $q$ growth from above, with $p \leq q$; this case is known as $p,…

I prove, under mild assumptions, that solutions to linear evolution equations admit sectorial solutions. The size of the sector depends on the regularity of the initial data. If it is regular enough the solution is holomorphic and unique…

The energy dependence for the singlet sector of Parton Distributions Functions (PDFs) is described by an entangled pair of ordinary linear differential equations. Although there are no exact analytic solutions, it is possible to provide…

This paper is concerned with the study of multiple positive solutions to the following elliptic problem involving a nonhomogeneous operator with nonstandard growth of $p$-$q$ type and singular nonlinearities \begin{equation*} \left\{…

In this paper we address the existence of time periodic solutions for the generalized inviscid SQG equation in the unit disc with homogeneous Dirichlet boundary condition when $\alpha\in (0,1)$. We show the existence of a countable family…