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Advanced Nonlinear Studies

Editor-in-Chief: Ahmad, Shair

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Volume 15, Issue 1


Spinorial Yamabe Type Equations on S3 via Conley Index

Takeshi Isobe
  • Department of Mathematics Graduate School of Science and Engineering Tokyo Institute of Technology 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, JAPAN
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Published Online: 2016-03-10 | DOI: https://doi.org/10.1515/ans-2015-0103


In this paper, we consider the existence of solutions to spinorial Yamabe type equations on S3 with a prescribed function H. We give a new condition about H under which at least one non-trivial solution exists. It is proved by a method based on Conley index theory applied to a reduced functional defined on a certain finite dimensional non-compact manifold. Our proof is also applicable to similar equations on Sm for all m ≥ 2.

Keywords: spinorial Yamabe equation; critical Sobolev exponent; variational method; Conley index

About the article

Received: 2013-09-16

Published Online: 2016-03-10

Published in Print: 2015-02-01

Citation Information: Advanced Nonlinear Studies, Volume 15, Issue 1, Pages 39–60, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2015-0103.

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