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The harmonic oscillator is a powerful model that can appear as a limit case when examining a nonlinear system. A well known fact is, that without driving, the inclusion of a friction term makes the origin of the phase space -- which is a…

Statistical Mechanics · Physics 2020-09-01 Daniel Schirdewahn

This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…

Optimization and Control · Mathematics 2017-01-03 Dongcai Su

We study the inverse problem of identifying a periodic potential perturbation of the Dirichlet Laplacian acting in an infinite cylindrical domain, whose cross section is assumed to be bounded. We prove log-log stable determination of the…

Analysis of PDEs · Mathematics 2016-01-21 Mourad Choulli , Yavar Kian , Eric Soccorsi

We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local…

Numerical Analysis · Mathematics 2025-10-20 Folkmar Bornemann , Christian Rasch

This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied problem is a nonlocal perturbation…

Classical Analysis and ODEs · Mathematics 2021-04-15 Alberto Cabada , Javier Iglesias

We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…

Analysis of PDEs · Mathematics 2016-05-24 Luciano Abadías , Marta de León-Contreras , José L. Torrea

We prove a stability estimate related to the multi-dimensional Borg-Levinson theorem of determining a potential from spectral data: the Dirichlet eigenvalues and the normal derivatives of the eigenfunctions on the boundary of a bounded…

Analysis of PDEs · Mathematics 2011-11-02 Mourad Choulli , Plamen Stefanov

The stability analysis of elastic rings subjected to various loading conditions is examined, focusing on stable and unstable configurations. The harmonic balance method is employed to investigate the stability range under different loading…

Classical Physics · Physics 2025-08-26 Muhammad Sami Siddiqui

We present a framework for solving the triharmonic equation over bilinearly parameterized planar multi-patch domains by means of isogeometric analysis. Our approach is based on the construction of a globally $C^2$-smooth isogeometric spline…

Numerical Analysis · Mathematics 2018-08-21 Mario Kapl , Vito Vitrih

It is by now well-known that one can recover a potential in the wave equation from the knowledge of the initial waves, the boundary data and the flux on a part of the boundary satisfying the Gamma-conditions of J.-L. Lions. We are…

Analysis of PDEs · Mathematics 2011-10-21 Lucie Baudouin , Sylvain Ervedoza

In this paper, we consider a biharmonic equation with respect to the Dirichlet problem on a domain of a locally finite graph. Using the variation method, we prove that the equation has two distinct solutions under certain conditions.

Analysis of PDEs · Mathematics 2022-05-17 Songbo Hou

In this note, we obtain the rigidity of the sharp Cheng-Yau gradient estimate for positive harmonic functions on surfaces with nonegative Gaussian curvature, the rigidity of the sharp Li-Yau gradient estimate for positive solutions to heat…

Differential Geometry · Mathematics 2024-11-05 Qixuan Hu , Guoyi Xu , Chengjie Yu

We show that the Dirichlet problem at infinity is unsolvable for the p-Laplace equation for any nonconstant continuous boundary data, for certain range of p>n, on an n-dimensional Cartan-Hadamard manifold constructed from a complete…

Differential Geometry · Mathematics 2016-03-30 Jingyi Chen , Yue Wang

We define and study the harmonic curves on domains in $\mathbb{R}^n$ into the first Heisenberg group $\mathbb{H}^1$. These are the $C^2$-regular mappings which are critical points of the second Dirichlet energy and satisfy the weak…

Analysis of PDEs · Mathematics 2024-07-30 Tomasz Adamowicz , Marco Capolli , Ben Warhurst

We discuss stability of spherically symmetric static solutions in Newtonian limit of Jordan, Brans-Dicke field equations. The behavior of the stable equilibrium solutions for the spherically symmetric configurations considered here, it…

General Relativity and Quantum Cosmology · Physics 2007-05-23 S. Kozyrev

We show how to compose robust stability tests for uncertain systems modeled as linear fractional representations and affected by various types of dynamic uncertainties. Our results are formulated in terms of linear matrix inequalities and…

Optimization and Control · Mathematics 2022-10-19 Tobias Holicki , Carsten W. Scherer

We show that for ultracontractive irreducible Dirichlet metric measure spaces, the Dirichlet spectrum is discrete for a restriction to any connected open set without any assumption on regularity of the boundary. The main applications…

Probability · Mathematics 2024-10-30 Marco Carfagnini , Maria Gordina , Alexander Teplyaev

We study an interplay between delay and discontinuous hysteresis in dynamical systems. After having established existence and uniqueness of solutions, we focus on the analysis of stability of periodic solutions. The main object we study is…

Dynamical Systems · Mathematics 2018-04-17 Pavel Gurevich , Eyal Ron

Fractional derivatives of Prabhakar type are capturing an increasing interest since their ability to describe anomalous relaxation phenomena (in dielectrics and other fields) showing a simultaneous nonlocal and nonlinear behaviour. In this…

Numerical Analysis · Mathematics 2020-08-13 Roberto Garrappa , Eva Kaslik

Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…

Dynamical Systems · Mathematics 2022-08-29 Sachin Bhalekar , Deepa Gupta