An existence results for a nonlinear boundary value problem via topological arguments. (English) Zbl 1368.58006

Sharaf, Khadijah

Topol. Methods Nonlinear Anal. 48, No. 1, 31-43 (2016).

This paper is concerned with the existence of a conformal scalar flat metric with prescribed boundary mean curvature on the unit \(n\)-dimensional ball. Combining topological and variational arguments, the author establishes the existence of solutions when the function to be prescribed satisfies at its critical points a non-degeneracy condition.

Reviewer: Vicenţiu D. Rădulescu (Craiova)

MSC:

58E05	Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
35J65	Nonlinear boundary value problems for linear elliptic equations
53C21	Methods of global Riemannian geometry, including PDE methods; curvature restrictions
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

conformal metric; boundary mean curvature; lack of compactness; critical points at infinity; stable and unstable manifolds; retracts by deformation