## Topological arguments in prescribing the scalar curvature under minimal boundary mean curvature condition on $$S^{n}_{+}$$.(English)Zbl 1224.18012

Summary: This paper is devoted to the prescribed scalar curvature problem under minimal boundary mean curvature condition on the standard $$n$$-dimensional half sphere with $$n\geq 3$$. Using tools related to the theory of critical points at infinity, we provide some topological conditions, on the level sets of a given positive function on $$S^{n}_{+}$$, under which we prove some existence results.

### MSC:

 18G35 Chain complexes (category-theoretic aspects), dg categories 35J61 Semilinear elliptic equations 35J25 Boundary value problems for second-order elliptic equations 57R58 Floer homology 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces