scholarly journals Dirichlet eigenvalue problems of irreversible Langevin diffusion

2021 ◽  
pp. 109242
Author(s):  
Nadia Belmabrouk ◽  
Mondher Damak ◽  
Nejib Yaakoubi
Keyword(s):  
Eigenvalue Problems ◽  
Dirichlet Eigenvalue ◽  
Langevin Diffusion

scholarly journals EIGENVALUE ESTIMATES FOR HIGHER ORDER ELLIPTIC EQUATIONS

1994 ◽  
Vol 25 (3) ◽  
pp. 267-278
Author(s):  
HSU-TUNG KU ◽  
MEI-CHIN KU ◽  
XIN-MIN ZHANG
Keyword(s):  
Lower Bound ◽  
Elliptic Equations ◽  
Eigenvalue Problems ◽  
Higher Order ◽  
Bounded Domains ◽  
Dirichlet Eigenvalue ◽  
Eigenvalue Estimates

In this paper, we obtain good lower bound estimates of eigenvalues for various Dirichlet eigenvalue problems of higher order elliptic equations on bounded domains in $\mathbb{R}^n$.

scholarly journals Multiple positive solutions for discrete p-Laplacian equations with potential term

2013 ◽  
Vol 7 (2) ◽  
pp. 327-342 ◽  
Author(s):  
Jong-Ho Kim ◽  
Jea-Hyun Park ◽  
June-Yub Lee
Keyword(s):  
Positive Solutions ◽  
Eigenvalue Problems ◽  
Existence Of Solutions ◽  
Growth Conditions ◽  
Multiple Positive Solutions ◽  
Source Terms ◽  
Dirichlet Eigenvalue ◽  
Nonlinear Source ◽  
Potential Term ◽  
Laplacian Equations

We study the existence of solutions to nonlinear discrete boundary value problems with the discrete p-Laplacian, potential, and nonlinear source terms. Using variational methods, we demonstrate that there exist at least two positive solutions. The existence strongly depends on the smallest positive eigenvalue of Dirichlet eigenvalue problems and the growth conditions of the source terms.

Convergence of variational eigenvalues and eigenfunctions to the Dirichlet problem for the p-Laplacian in domains with fine-grained boundary

2010 ◽  
Vol 140 (3) ◽  
pp. 573-596
Author(s):  
Pavel Drábek ◽  
Yuliya Namlyeyeva ◽  
Šárka Nečasová
Keyword(s):  
Eigenvalue Problems ◽  
Additional Term ◽  
Expansion Method ◽  
Critical Levels ◽  
Eigenvalues And Eigenfunctions ◽  
Dirichlet Eigenvalue ◽  
Perforated Domains ◽  
Fine Grained ◽  
New Equation ◽  
Asymptotic Expansion Method

We study the problem of the homogenization of Dirichlet eigenvalue problems for the p-Laplace operator in a sequence of perforated domains with fine-grained boundary. Using the asymptotic expansion method, we derive the homogenized problem for the new equation with an additional term of capacity type. Moreover, we show that a sequence of eigenvalues for the problem in perforated domains converges to the corresponding critical levels of the homogenized problem.

scholarly journals Estimates for lower bounds of eigenvalues of the poly-Laplacian and the quadratic polynomial operator of the Laplacian

2013 ◽  
Vol 143 (6) ◽  
pp. 1147-1162 ◽  
Author(s):  
Qing-Ming Cheng ◽  
He-Jun Sun ◽  
Guoxin Wei ◽  
Lingzhong Zeng
Keyword(s):  
Lower Bounds ◽  
Eigenvalue Problems ◽  
Quadratic Polynomial ◽  
Polynomial Operator ◽  
Dirichlet Eigenvalue

In this paper, we investigate the Dirichlet eigenvalue problems of the poly-Laplacian with any order and the quadratic polynomial operator of the Laplacian. We give some estimates for lower bounds of the sums of their first k eigenvalues.

scholarly journals Eigenvalue bounds of mixed Steklov problems

2019 ◽  
Vol 22 (02) ◽  
pp. 1950008 ◽  
Author(s):  
Asma Hassannezhad ◽  
Ari Laptev
Keyword(s):  
Eigenvalue Problem ◽  
Fractional Laplacian ◽  
Eigenvalue Problems ◽  
Asymptotic Results ◽  
Riesz Means ◽  
Dirichlet Eigenvalue ◽  
Eigenvalue Bounds ◽  
Steklov Eigenvalue ◽  
Dirichlet Eigenvalue Problem ◽  
Neumann Eigenvalue

We study bounds on the Riesz means of the mixed Steklov–Neumann and Steklov–Dirichlet eigenvalue problem on a bounded domain [Formula: see text] in [Formula: see text]. The Steklov–Neumann eigenvalue problem is also called the sloshing problem. We obtain two-term asymptotically sharp lower bounds on the Riesz means of the sloshing problem and also provide an asymptotically sharp upper bound for the Riesz means of mixed Steklov–Dirichlet problem. The proof of our results for the sloshing problem uses the average variational principle and monotonicity of sloshing eigenvalues. In the case of Steklov–Dirichlet eigenvalue problem, the proof is based on a well-known bound on the Riesz means of the Dirichlet fractional Laplacian, and an inequality between the Dirichlet and Navier fractional Laplacian. The two-term asymptotic results for the Riesz means of mixed Steklov eigenvalue problems are discussed in the Appendix which in particular show the asymptotic sharpness of the bounds we obtain.

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