Yacoub, Ridha Topological arguments in prescribing the scalar curvature under minimal boundary mean curvature condition on \(S^{n}_{+}\). (English) Zbl 1224.18012 Differ. Integral Equ. 21, No. 5-6, 459-476 (2008). 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. Cited in 1 Document 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 Keywords:mean curvature; positive solution; semilinear elliptic equation; critical point PDFBibTeX XMLCite \textit{R. Yacoub}, Differ. Integral Equ. 21, No. 5--6, 459--476 (2008; Zbl 1224.18012)