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Following the study of complex elliptic-function-type asymptotic behaviours of the Painlev\'e equations by Boutroux and Joshi and Kruskal for $P_I$ and $P_{II}$, we provide new results for elliptic-function-type behaviours admitted by…

Exactly Solvable and Integrable Systems · Physics 2018-08-01 Nalini Joshi , Elynor Liu

Asymptotic behaviour of eigenvalues and eigenfunctions of a stiff problem is described in the case of the fourth-order ordinary differential operator. Considering the stiffness coefficient that depends on a small parameter epsilon and…

Spectral Theory · Mathematics 2008-10-02 N. Babych , Yu. Golovaty

We study asymptotic behavior of the bottom point of the spectrum of convolution type operators in environments with locally periodic microstructure. We show that its limit is described by an additive eigenvalue problem for Hamilton-Jacobi…

Analysis of PDEs · Mathematics 2024-01-31 Andrey Piatnitski , Volodymyr Rybalko

The paper is concerned with asymptotic properties of the principal components analysis of functional data. The currently available results assume the existence of the fourth moment. We develop analogous results in a setting which does not…

Statistics Theory · Mathematics 2018-12-10 Piotr Kokoszka , Stilian Stoev , Qian Xiong

In this paper, we are concerned with the asymptotic behavior of weak solutions to certain elliptic and parabolic problems involving the fractional $p$-Laplacian in cylindrical domains that become unbounded in one direction. The nonlocal…

Analysis of PDEs · Mathematics 2025-10-24 Tahir Boudjeriou , Prosenjit Roy

In this note we obtain an asymptotic estimate for growth behavior of variational eigenvalues of the $p-$fractional eigenvalue problem on a smooth bounded domain with Dirichlet boundary condition.

Analysis of PDEs · Mathematics 2021-11-08 Ariel Salort , Eugenio Vecchi

A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability of the Hermitian quadratic form, the direct integral structure of…

Functional Analysis · Mathematics 2022-07-11 Alberto Ibort , José G. Llavona , Fernando Lledó , Juan Manuel Pérez-Pardo

We will discuss the asymptotic behaviour of the eigenvalues of Schr\"{o}dinger operator with a matrix potential defined by Neumann boundary condition in $L_2^m(F)$, where $F$ is $d$-dimensional rectangle and the potential is a $m \times m$…

Spectral Theory · Mathematics 2015-05-20 Sedef Karakılıç , Setenay Akduman , Didem Coşkan

We consider the elasticity operator with zero Poisson's ratio on an infinite strip and an infinite plate with a horizontal crack. We prove an asymptotic formula for the distance of the embedded eigenvalues to some spectral threshold of the…

Spectral Theory · Mathematics 2015-11-20 André Hänel , Timo Weidl

We study the asymptotic behavior of Multiple Meixner polynomials of first and second kind, respectively (see J. Arves\'u et al. J. Comput. Appl. Math., 153, (2003)). We use an algebraic function formulation for the solution of the…

Classical Analysis and ODEs · Mathematics 2012-07-03 A. Aptekarev , J. Arvesú

In the present paper, we study the asymptotic properties of the semi-exponential Post-Widder operator. It is connected with $p(x) = x^2$. The main result is a pointwise complete asymptotic expansion valid for locally smooth functions of…

Classical Analysis and ODEs · Mathematics 2025-09-17 Ulrich Abel , Octavian Agratini , Radu Paltanea

Boundary value problem for a fractional power of an elliptic operator is considered. An integral representation by means of a standard solution problem for parabolic equations is used to solve such problems. Quadrature generalized…

Numerical Analysis · Mathematics 2019-10-25 Petr N. Vabishchevich

This paper is concerned with the asymptotic expansions of the amplitude of the solution of the Helmholtz equation. The original expansions were obtained using a pseudo-differential decomposition of the Dirichlet to Neumann operator. This…

Analysis of PDEs · Mathematics 2016-12-13 Souaad Lazergui , Yassine Boubendir

This paper completes and partially improves some of the results of [arXiv:0809.5002] about the asymptotic behavior of solutions of linear and nonlinear elliptic equations with singular coefficients via an Almgren type monotonicity formula

Analysis of PDEs · Mathematics 2011-02-22 Veronica Felli , Alberto Ferrero , Susanna Terracini

We consider a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. In a previous paper we have found mass-preserving, nonnegative weak solutions of the equation satisfying energy…

Analysis of PDEs · Mathematics 2010-04-08 Luis Caffarelli , Juan Luis Vazquez

Let $F$ be a Banach space and $L(F)$ be the set of all its bounded linear operators. In this note, we are interested in the asymptotic behavior (recurrence and chain recurrence) of the solution of the following initial value problem…

Dynamical Systems · Mathematics 2009-08-21 Mauro Patrão

In this paper, we first investigate the monotonicity and limit problem of the fractional integral functions. By fixed point theorem and these new results of the fractional integral functions, we present that the Riemann-Liouville fractional…

Classical Analysis and ODEs · Mathematics 2023-08-30 Tao Zhu

This paper considers boundary value problems for a class of singular elliptic operators which appear naturally in the study of asymptotically anti-de Sitter (aAdS) spacetimes. These problems involve a singular Bessel operator acting in the…

Analysis of PDEs · Mathematics 2018-08-14 Oran Gannot

We consider the spectrum of the Laplace operator on 3D rod structures, with a small cross section depending on a small parameter $\varepsilon$. The boundary conditions are of Dirichlet type on the basis of this structure and Neumann on the…

Analysis of PDEs · Mathematics 2025-05-16 Pablo Benavent-Ocejo , Delfina Gómez , María-Eugenia Pérez-Martínez

We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the…

Differential Geometry · Mathematics 2019-07-25 Christian Baer , Werner Ballmann