Abstract
Abstract 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.
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