In this paper, we investigate a class of nonlinear eigenvalue problems resulting from quantum physics. We first prove that for any open set G , there exists an eigenfunction cannot be polynomial on which may reviewed as refinement the classic unique continuation property. Then apply non-polynomial behavior to show adaptive finite element approximations are convergent even if initial mesh is not...

We prove a Fatou-type theorem and its converse for certain positive eigenfunctions of the Laplace–Beltrami operator $${\mathcal {L}}$$ on Harmonic NA group. show that eigenfunction u with eigenvalue $$\beta ^2-\rho ^2$$ , where \in (0,\infty )$$ has admissible limit in sense Korányi, precisely at those boundary points strong derivative measure exists. Moreover, are same. This extends result Ram...

We propose an analytical method to analyze the propagation of a once-and-for-all shock in broad class sticky price models. The is based on eigenvalue- eigenfunction representation dynamics cross-sectional distribution firms’ desired adjustments. A key novelty that, under assumptions that are appropriate for low-inflation economies, we can approximate whole profile impulse response any moment ...

We investigate several 2D and 3D cases of the classical eigenvalue problem that arises in hydrodynamics and is referred to as the sloshing problem. In particular, for a domain W ⊂ R (canal’s crosssection), where ∂W = F ∪ B and F (cross-section of the free surface of fluid) is an interval of the x-axis, whereas B (bottom’s cross-section) is the graph of a negative function, the following result ...

Thermoelastic expansion due to frictional heating causes significant changes in contact pressure and temperature in energy dissipation systems uch as brakes and clutches. Finite element analysis of such systems tends to be extremely computer-intensive. We here present an alternative mplementation of the transient problem, based on the expression of the temperature and stress fields as modal exp...

We prove the convergence of an adaptive linear finite element method for computing eigenvalues and eigenfunctions of second order symmetric elliptic partial differential operators. The weak form is assumed to yield a bilinear form which is bounded and coercive in H1. Each step of the adaptive procedure refines elements in which a standard a posteriori error estimator is large and also refines e...

We prove the convergence of an adaptive linear finite element method for computing eigenvalues and eigenfunctions of second order symmetric elliptic partial differential operators. The weak form is assumed to yield a bilinear form which is bounded and coercive in H. Each step of the adaptive procedure refines elements in which a standard a posteriori error estimator is large and also refines el...

This paper is concerned with the nonlinear multiparameter elliptic eigenvalue problem u′′(r) + N − 1 r u′(r) + μu(r)− k ∑ i=1 λifi(u(r)) = 0, 0 < r < 1, u(r) > 0, 0 ≤ r < 1, u′(0) = 0, u(1) = 0, where N ≥ 1, k ∈ N and μ, λi ≥ 0 (1 ≤ i ≤ k) are parameters. The aim of this paper is to study the asymptotic properties of eigencurve μ(λ, α) = μ(λ1, λ2, · · · , λk, α) with emphasis on the phenomenon ...

In this article, by extending the method of [AC] we prove a sharp estimate on the expansion modulus of the gradient of the logarithm of the parabolic kernel to the Schördinger operator with convex potential on a bounded convex domain. The result improves an earlier work of Brascamp-Lieb which asserts the log-concavity of the parabolic kernel. We also give an alternate proof to a corresponding e...

We study the max-plus equation P þ cðxÞ 1⁄4 max xpspM ðHðsÞ þ cðgðsÞÞÞ; xA1⁄20;M ; ð*Þ where H : 1⁄20;M -ð N;NÞ and g : 1⁄20;M -1⁄20;M are given functions. The function c : 1⁄20;M -1⁄2 N;NÞ and the quantity P are unknown, and are, respectively, an eigenfunction and additive eigenvalue. Eigensolutions c are known to describe the asymptotics of certain solutions of singularly perturbed differenti...