Fundamental solutions for Schrödinger operators with general inverse square potentials

Huyuan Chen; Suad Alhomedan; Hichem Hajaiej; Peter A. Markowich

doi:10.1080/00036811.2017.1286648

Fundamental solutions for Schrödinger operators with general inverse square potentials

Huyuan Chen, Suad Alhomedan, Hichem Hajaiej, Peter A. Markowich

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6 Scopus citations

Abstract

In this paper, we clarify the fundamental solutions for Schrödinger operators given as (Formula presented.), where the potential V is a general inverse square potential in (Formula presented.) with (Formula presented.). In particular, letting (Formula presented.),(Formula presented.) where (Formula presented.), we discuss the existence and nonexistence of positive fundamental solutions for Hardy operator (Formula presented.), which depend on the parameter t.

Original language	English (US)
Pages (from-to)	787-810
Number of pages	24
Journal	Applicable Analysis
Volume	97
Issue number	5
DOIs	https://doi.org/10.1080/00036811.2017.1286648
State	Published - Mar 17 2017

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: H. Chen is supported by NNSF of China [grant number 11401270], [grant number 11661045]; the Jiangxi Provincial Natural Science Foundation [grant number 20161ACB20007]; SRF for ROCS, SEM from Ministry of Education in China.

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10.1080/00036811.2017.1286648

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title = "Fundamental solutions for Schr{\"o}dinger operators with general inverse square potentials",

abstract = "In this paper, we clarify the fundamental solutions for Schr{\"o}dinger operators given as (Formula presented.), where the potential V is a general inverse square potential in (Formula presented.) with (Formula presented.). In particular, letting (Formula presented.),(Formula presented.) where (Formula presented.), we discuss the existence and nonexistence of positive fundamental solutions for Hardy operator (Formula presented.), which depend on the parameter t.",

author = "Huyuan Chen and Suad Alhomedan and Hichem Hajaiej and Markowich, {Peter A.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: H. Chen is supported by NNSF of China [grant number 11401270], [grant number 11661045]; the Jiangxi Provincial Natural Science Foundation [grant number 20161ACB20007]; SRF for ROCS, SEM from Ministry of Education in China.",

year = "2017",

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doi = "10.1080/00036811.2017.1286648",

language = "English (US)",

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T1 - Fundamental solutions for Schrödinger operators with general inverse square potentials

AU - Chen, Huyuan

AU - Alhomedan, Suad

AU - Hajaiej, Hichem

AU - Markowich, Peter A.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: H. Chen is supported by NNSF of China [grant number 11401270], [grant number 11661045]; the Jiangxi Provincial Natural Science Foundation [grant number 20161ACB20007]; SRF for ROCS, SEM from Ministry of Education in China.

PY - 2017/3/17

Y1 - 2017/3/17

N2 - In this paper, we clarify the fundamental solutions for Schrödinger operators given as (Formula presented.), where the potential V is a general inverse square potential in (Formula presented.) with (Formula presented.). In particular, letting (Formula presented.),(Formula presented.) where (Formula presented.), we discuss the existence and nonexistence of positive fundamental solutions for Hardy operator (Formula presented.), which depend on the parameter t.

AB - In this paper, we clarify the fundamental solutions for Schrödinger operators given as (Formula presented.), where the potential V is a general inverse square potential in (Formula presented.) with (Formula presented.). In particular, letting (Formula presented.),(Formula presented.) where (Formula presented.), we discuss the existence and nonexistence of positive fundamental solutions for Hardy operator (Formula presented.), which depend on the parameter t.

UR - http://hdl.handle.net/10754/623837

UR - http://www.tandfonline.com/doi/full/10.1080/00036811.2017.1286648

UR - http://www.scopus.com/inward/record.url?scp=85015666526&partnerID=8YFLogxK

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DO - 10.1080/00036811.2017.1286648

M3 - Article

SN - 0003-6811

VL - 97

SP - 787

EP - 810

JO - Applicable Analysis

JF - Applicable Analysis

IS - 5

ER -

Fundamental solutions for Schrödinger operators with general inverse square potentials

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