Cherrier–Escobar problem for the elliptic Schrödinger-to-Neumann map

Mohammed Aldawood; Cheikh Birahim Ndiaye

doi:10.1016/j.na.2024.113525

Cherrier–Escobar problem for the elliptic Schrödinger-to-Neumann map

Mohammed Aldawood
, Cheikh Birahim Ndiaye

Howard University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we study a Cherrier–Escobar problem for the extended problem corresponding to the elliptic Schrödinger-to-Neumann map on a compact 3-dimensional Riemannian manifold with boundary. Using the algebraic topological argument of Bahri and Coron (1988), we show solvability under the assumption that the extended problem corresponding to the elliptic Schrödinger-to-Neumann map has a positive first eigenvalue and a positive Green's function.

Original language	English
Article number	113525
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	243
DOIs	https://doi.org/10.1016/j.na.2024.113525
State	Published - Jun 2024
Externally published	Yes

Keywords

Barycenter technique
Elliptic Schrödinger-to-Neumann map
Inter-action estimates
PS-sequences
Self-action estimates

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10.1016/j.na.2024.113525

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title = "Cherrier–Escobar problem for the elliptic Schr{\"o}dinger-to-Neumann map",

abstract = "In this paper, we study a Cherrier–Escobar problem for the extended problem corresponding to the elliptic Schr{\"o}dinger-to-Neumann map on a compact 3-dimensional Riemannian manifold with boundary. Using the algebraic topological argument of Bahri and Coron (1988), we show solvability under the assumption that the extended problem corresponding to the elliptic Schr{\"o}dinger-to-Neumann map has a positive first eigenvalue and a positive Green's function.",

keywords = "Barycenter technique, Elliptic Schr{\"o}dinger-to-Neumann map, Inter-action estimates, PS-sequences, Self-action estimates",

author = "Mohammed Aldawood and Ndiaye, \{Cheikh Birahim\}",

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year = "2024",

month = jun,

doi = "10.1016/j.na.2024.113525",

language = "English",

volume = "243",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

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AU - Aldawood, Mohammed

AU - Ndiaye, Cheikh Birahim

PY - 2024/6

Y1 - 2024/6

N2 - In this paper, we study a Cherrier–Escobar problem for the extended problem corresponding to the elliptic Schrödinger-to-Neumann map on a compact 3-dimensional Riemannian manifold with boundary. Using the algebraic topological argument of Bahri and Coron (1988), we show solvability under the assumption that the extended problem corresponding to the elliptic Schrödinger-to-Neumann map has a positive first eigenvalue and a positive Green's function.

AB - In this paper, we study a Cherrier–Escobar problem for the extended problem corresponding to the elliptic Schrödinger-to-Neumann map on a compact 3-dimensional Riemannian manifold with boundary. Using the algebraic topological argument of Bahri and Coron (1988), we show solvability under the assumption that the extended problem corresponding to the elliptic Schrödinger-to-Neumann map has a positive first eigenvalue and a positive Green's function.

KW - Barycenter technique

KW - Elliptic Schrödinger-to-Neumann map

KW - Inter-action estimates

KW - PS-sequences

KW - Self-action estimates

UR - https://www.scopus.com/pages/publications/85188230575

U2 - 10.1016/j.na.2024.113525

DO - 10.1016/j.na.2024.113525

M3 - Article

AN - SCOPUS:85188230575

SN - 0362-546X

VL - 243

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

M1 - 113525

ER -

Cherrier–Escobar problem for the elliptic Schrödinger-to-Neumann map

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Keywords

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