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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the following semilinear elliptic equation on a strip: \[\left\{{array}{l} \Delta u-u + u^p=0 \ {in} \ \R^{N-1} \times (0, L), u>0,\frac{\partial u}{\partial \nu}=0 \ {on} \ \partial (\R^{N-1} \times (0, L)){array} \right.\] where $ 1< p\leq \frac{N+2}{N-2}$. When $ 1<p<\frac{N+2}{N-2}$, it is shown that there exists a unique $L_{*} >0$ such thatfor $L \leq L_{*}$, the least energy solution is trivial, i.e., doesn't dependon $x_N$, and for $L >L_{*}$, the least energy solution is nontrivial. When $N\geq 4, p=\frac{N+2}{N-2}$, it is shown that there are two numbers$L_{*}<L_{**}$ such that the least energy solution is trivial when $L \leqL_{*}$, the least energy solution is nontrivial when $L \in (L_{*}, L_{**}]$,and the least energy solution does not exist when $L >L_{**}$. A connectionwith Delaunay surfaces in CMC theory is also made.

On least energy solutions to a semilinear elliptic equation in a strip