REVIEW 1 cited by
Local bifurcation diagrams and degenerate solutions of Yamabe-type equations
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
We study positive solutions of the equation $-\Delta_g u + \lambda u = \lambda u^q$, with $\lambda >0$, $q>1$ on the round sphere $\mathbb{S}^n$ . We reduce the equation to an ordinary differential equation by considering isoparametric functions and apply bifurcation theory. We study when the corresponding bifurcation points are transcritical. We apply this result to show the existence of degenerate solutions to the equation and to study multiplicity results for conformal constant scalar curvature metrics.
Forward citations
Cited by 1 Pith paper
-
Fractional $Q$-curvature on the sphere and optimal partitions
Symmetry reduces the fractional Q-curvature optimal partition problem on the sphere to one dimension, yielding a minimizer made of disjoint spherical shells.
Discussion (0). Continue with ORCID to comment.