Fundamental solutions for Schrödinger operators with general inverse square potentials

Abstract

In this paper, we clarify the fundamental solutions for Schrödinger operators given as , where the potential V is a general inverse square potential in with . In particular, letting ,

where , we discuss the existence and nonexistence of positive fundamental solutions for Hardy operator , which depend on the parameter t.

Keywords:

• Inverse square potentials
• fundamental solution
• nonexistence

AMS Subject Classifications:

• 35A08
• 35D99
• 35B53

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

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.