Sharp estimates for the first eigenvalue of Schrödinger operator in the unit sphere

2021 ◽  
Author(s):  
Jiabin Yin ◽  
Xuerong Qi
Keyword(s):  
Schrödinger Operator ◽  
Unit Sphere ◽  
First Eigenvalue ◽  
Schrodinger Operator ◽  
Sharp Estimates ◽  
The First Eigenvalue

scholarly journals Spectral characterization and Schrödinger operator of space-like submanifolds

2015 ◽  
Vol 23 (2) ◽  
pp. 241-257
Author(s):  
Shichang Shu ◽  
Tianmin Zhu
Keyword(s):  
Schrödinger Operator ◽  
Schrödinger Operators ◽  
Spectral Characterization ◽  
Schrodinger Operators ◽  
First Eigenvalue ◽  
Schrodinger Operator ◽  
De Sitter ◽  
Totally Umbilical ◽  
The First Eigenvalue ◽  
Spectral Characterizations

Abstract In this paper, we would like to study space-like submanifolds in a de Sitter spaces Spn+p(1). We define and discuss three Schrödinger operators LH, LR, LR/H and obtain some spectral characterizations of totally umbilical space-like submanifolds in terms of the first eigenvalue of the Schrödinger operators LH, LR and LR/H respectively.

The first eigenvalue for a quasilinear Schrödinger operator and its application

2017 ◽  
Vol 97 (4) ◽  
pp. 499-512 ◽  
Author(s):  
Olimpio Hiroshi Miyagaki ◽  
Sandra Imaculada Moreira ◽  
Ricardo Ruviaro
Keyword(s):  
Schrödinger Operator ◽  
First Eigenvalue ◽  
Schrodinger Operator ◽  
The First Eigenvalue

scholarly journals Sharp estimates for the first p-Laplacian eigenvalue and for the p-torsional rigidity on convex sets with holes

2020 ◽  
Vol 26 ◽  
pp. 111 ◽  
Author(s):  
Gloria Paoli ◽  
Gianpaolo Piscitelli ◽  
Leonardo Trani
Keyword(s):  
Boundary Conditions ◽  
Convex Sets ◽  
Torsional Rigidity ◽  
Neumann Boundary ◽  
Robin Boundary Conditions ◽  
First Eigenvalue ◽  
Laplacian Eigenvalue ◽  
Sharp Estimates ◽  
The First Eigenvalue ◽  
Robin Boundary

We study, in dimension n ≥ 2, the eigenvalue problem and the torsional rigidity for the p-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions. We prove that the annulus maximizes the first eigenvalue and minimizes the torsional rigidity when the measure and the external perimeter are fixed.

Existence of the first eigenvalue of the eigenvalue problem for the Laplace-Beltrami operator on the unit sphere

2018 ◽  
Vol 55 (3) ◽  
pp. 374-382
Author(s):  
Mariusz Bodzioch ◽  
Mikhail Borsuk ◽  
Sebastian Jankowski
Keyword(s):  
Eigenvalue Problem ◽  
Asymptotic Behaviour ◽  
Unit Sphere ◽  
Beltrami Operator ◽  
Positive Eigenvalue ◽  
Conical Point ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
Asymptotic Behaviour Of Solutions ◽  
Oblique Derivative Problems

In this paper we formulate and prove that there exists the first positive eigenvalue of the eigenvalue problem with oblique derivative for the Laplace-Beltrami operator on the unit sphere. The firrst eigenvalue plays a major role in studying the asymptotic behaviour of solutions of oblique derivative problems in cone-like domains. Our work is motivated by the fact that the precise solutions decreasing rate near the boundary conical point is dependent on the first eigenvalue.

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