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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study existence and properties of ground states for the nonlinearSchr\"odinger equation with combined power nonlinearities \[ -\Delta u= \lambdau + \mu |u|^{q-2} u + |u|^{p-2} u \qquad \text{in $\mathbb{R}^N$, $N \ge 1$,}\] having prescribed mass \[ \int_{\mathbb{R}^N} |u|^2 = a^2. \] Underdifferent assumptions on $q<p$, $a>0$ and $\mu \in \mathbb{R}$ we prove severalexistence and stability/instability results. In particular, we consider caseswhen \[ 2<q \le 2+ \frac{4}{N} \le p<2^*, \quad q \neq p, \] i.e. the twononlinearities have different character with respect to the $L^2$-criticalexponent. These cases present substantial differences with respect to purelysubcritical or supercritical situations, which were already studied in theliterature.  We also give new criteria for global existence and finite time blow-up in theassociated dispersive equation.

Normalized ground states for the NLS equation with combined nonlinearities