Abstract
In this paper, we consider a fractional Nirenberg-type problem involving σ-exponent of the Laplacian on the standard n-dimensional spheres . Using an algebraic topological method and the theory of the critical points at infinity, we provide a variety of classes of functions that can be realized as the σ-curvature on n-dimensional sphere. MSC: 35M30, 35Q74, 74A15, 74A60, 74M25.
Highlights
1 Introduction and main results Let (Sn, g) be the standard sphere of dimension n, n ≥ and K be a positive function on Sn
Several studies have been performed for classical elliptic equations similar to
The following propositions characterize the critical points at infinity of the associated variational problem
Summary
Introduction and main resultsLet (Sn, g) be the standard sphere of dimension n, n ≥ and K be a positive function on Sn. [ ] Let K be a positive function satisfying the following (nd) condition: (nd): Assume that K is a smooth function on S having only non-degenerate critical points with
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