Related papers: Linear Difference Equations with a Transition Poin…

As $\varepsilon$ goes to zero, the unique solution of the scalar advection-diffusion equation $y^{\varepsilon}_t-\varepsilon y^{\varepsilon}_{xx} + M y^{\varepsilon}_x=0$, $(x,t)\in (0,1)\times (0,T)$ submitted to Dirichlet boundary…

We develop a unified analytical and computational framework for the generalized Abel ordinary differential equation $y^{\prime }(x)=a_n(x)\bigl(% y^n+\lambda_{n-1}(x)y^{n-1}+\dots+\lambda_0(x)\bigr)$ of arbitrary degree $% n\ge1$ on the…

In this paper we study a generalized class of Maxwell-Boltzmann equations which in addition to the usual collision term contains a linear deformation term described by a matrix A. This class of equations arises, for instance, from the…

The paper deals with an integrodifferential operator which models numerous phenomena in superconductivity, in biology and in viscoelasticity. Initialboundary value problems with Neumann, Dirichlet and mixed boundary conditions are analyzed.…

Asymptotic expansions are given for large values of $n$ of the generalized Bernoulli polynomials $B_n^\mu(z)$ and Euler polynomials $E_n^\mu(z)$. In a previous paper L\'opez and Temme (1999) these polynomials have been considered for large…

We establish conditions guaranteeing that all eventually positive increasing solutions of a half-linear delay differential equation are regularly varying and derive precise asymptotic formulae for them. The results here presented are new…

A system of nonlinear differential equations $x^{1+\gamma}\frac{dY}{dx}= F_0(x)+A(x)Y+F(x,Y)$ is considered. We study more precisely the meaning of asymptotic expansion of transformations and solutions than preceding pioneering works, by…

The asymptotic expansion of digamma function is a starting point for the derivation of approximants for harmonic sums or Euler-Mascheroni constant. It is usual to derive such approximations as values of logarithmic function, which leads to…

We construct asymptotic expansions for the normalised incomplete gamma function $Q(a,z)=\Gamma(a,z)/\Gamma(a)$ that are valid in the transition regions, including the case $z\approx a$, and have simple polynomial coefficients. For Bessel…

In this paper we obtain the precise description of the asymptotic behavior of the solution $u$ of $$ \partial_t u+(-\Delta)^{\frac{\theta}{2}}u=0\quad\mbox{in}\quad{\bf R}^N\times(0,\infty), \qquad u(x,0)=\varphi(x)\quad\mbox{in}\quad{\bf…

We study asymptotic behaviors of positive solutions to the Yamabe equation and the $\sigma$k-Yamabe equation near isolated singular points and establish expansions up to arbitrary orders. Such results generalize an earlier pioneering work…

We study the distribution of the length of longest monotone subsequences in random (fixed-point free) involutions of $n$ integers as $n$ grows large, establishing asymptotic expansions in powers of $n^{-1/6}$ in the general case and in…

We consider the Neumann problem for the equation $u_{xx}+\lambda f(u)=0$ in the punctured interval $(-1,1) \setminus \{0\}$, where $\lambda>0$ is a bifurcation parameter and $f(u)=u-u^3$. At $x=0$, we impose the conditions…

We prove an asymptotic formula for the second moment of automorphic L-functions of even weight and prime power level. The error term is estimated uniformly in all parameters: level, weight, shift and twist.

We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problem \begin{equation*} \label{eq-1} \begin{gathered} {u^{\prime \prime}}(t)+f(t, u(t))=0,\ 0<t<T, \\…

We investigate the asymptotic behavior of solutions to a class of weighted quasilinear elliptic equations which arise from the Euler--Lagrange equation associated with the Caffarelli--Kohn--Nirenberg inequality. We obtain sharp pointwise…

We consider asymptotically stable scalar difference equations with unit-norm initial conditions. First, it is shown that the solution may happen to deviate far away from the equilibrium point at finite time instants prior to converging to…

This paper develops further and systematically the asymptotic expansion theory that was initiated by Foias and Saut in [11]. We study the long-time dynamics of a large class of dissipative systems of nonlinear ordinary differential…

Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…

This paper addresses the problem of finding an asymptotic solution for first and second order integro-differential equations containing an arbitrary kernel, by evaluating the corresponding inverse Laplace and Fourier transforms. The aim of…