English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let $(M,g)$ be a closed Riemannian manifold of dimension $n\geq 3$ and $x_0\in M$ be an isolated local minimum of the scalar curvature $s_g$ of $g$. Forany positive integer $k$ we prove that for $\epsilon >0$ small enough thesubcritical Yamabe equation $-\epsilon^2 \Delta u +(1+ c_{N} \ \epsilon^2 s_g )u = u^q$ has a positive $k$-peaks solution which concentrate around $x_0$,assuming that a constant $\beta$ is non-zero. In the equation $c_N =\frac{N-2}{4(N-1)}$ for an integer $N>n$ and $q= \frac{N+2}{N-2}$. The constant$\beta$ depends on $n$ and $N$, and can be easily computed numerically, beingnegative in all cases considered. This provides solutions to the Yamabeequation on Riemannian products $(M\times X , g+ \epsilon^2 h )$, where $(X,h)$is a Riemannian manifold with constant positive scalar curvature. We also provethat solutions with small energy only have one local maximum.

Multipeak solutions for the Yamabe equation