Results 21 to 30 of about 873 (53)

The "hot spots" conjecture on the Vicsek set

Demonstratio Mathematica, 2019
We prove the “hot spots” conjecture on the Vicsek set. Specifically, we will show that every eigenfunction of the second smallest eigenvalue of the Neumann Laplacian on the Vicsek set attains its maximum and minimum on the boundary.
Ionescu Marius, Savage Thomas L.
doaj   +1 more source

Multiplicity of solutions to discrete inclusions with the p(k)-Laplace type equations

Nonautonomous Dynamical Systems, 2018
In this article, we prove the existence and multiplicity of solutions to discrete inclusions with the p(k)-Laplace type equations. We are interested in the existence of three solutions with the aid of linking arguments and using a three critical points ...
Ouaro Stanislas, Zoungrana Malick
doaj   +1 more source

A Spectral Gap Estimate and Applications

, 2017
We consider the Schr\"odinger operator $$-\frac{d^2}{d x^2} + V \qquad \mbox{on an interval}~~[a,b]~\mbox{with Dirichlet boundary conditions},$$ where $V$ is bounded from below and prove a lower bound on the first eigenvalue $\lambda_1$ in terms of ...
Georgiev, Bogdan, Mukherjee, Mayukh, Steinerberger, Stefan   +2 more
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Principal spectral theory and asymptotic behavior of the spectral bound for partially degenerate nonlocal dispersal systems

Advanced Nonlinear Studies
The purpose of this paper is to investigate the principal spectral theory and asymptotic behavior of the spectral bound for cooperative nonlocal dispersal systems, specifically focusing on the case where partial diffusion coefficients are zero, referred ...
Zhang Lei
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Spectral asymptotics for the fourth-order operator with periodic coefficients [PDF]

arXiv, 2022
We consider the self-adjoint fourth-order operator with real $1$-periodic coefficients on the unit interval. The spectrum of this operator is discrete. We determine the high energy asymptotics for its eigenvalues.
arxiv  

On the solvability of discrete nonlinear Neumann problems involving the p(x)-Laplacian

Advances in Difference Equations, 2011
In this article, we prove the existence and uniqueness of solutions for a family of discrete boundary value problems for data f which belongs to a discrete Hilbert space W. 2010 Mathematics Subject Classification: 47A75; 35B38; 35P30; 34L05; 34L30.
Ouaro Stanislas, Guiro Aboudramane, Nyanquini Ismael   +2 more
doaj  

On spectral estimates for the Schr\"odinger operators in global dimension 2

, 2012
The problem of finding eigenvalue estimates for the Schr\"odinger operator turns out to be most complicated for the dimension 2. Some important results for this case have been obtained recently.
Rozenblum, Grigori, Solomyak, Michael
core   +1 more source

Quantitative bounds on the discrete spectrum of non self-adjoint quantum magnetic Hamiltonians [PDF]

, 2016
We establish Lieb-Thirring type inequalities for non self-adjoint relatively compact perturbations of certain operators of mathematical physics. We apply our results to quantum Hamiltonians of Schr{\"o}dinger and Pauli with constant magnetic field of ...
Sambou, Diomba
core  

Landau dispersion relationship in self-consistent field theory [PDF]

arXiv, 2019
The spectral problem is studied associated with Maxwell-Boltzmann equations describing collisionless plasma. Formula for instability index is obtained and effective conditions of two-stream instability are given.
arxiv  

On the remainder term of the Berezin inequality on a convex domain

, 2016
We study the Dirichlet eigenvalues of the Laplacian on a convex domain in $\mathbb{R}^n$, with $n\geq 2$. In particular, we generalize and improve upper bounds for the Riesz means of order $\sigma\geq 3/2$ established in an article by Geisinger, Laptev ...
Larson, Simon
core   +1 more source