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

Normalized ground state solutions (NGSS) of Schrodinger equations (SE) haveattracted the attention of many research groups during the last decades. Thisis essentially due to their relevance in many fields in physics andengineering, where the stable and most attractive solutions happen to be thenormalized ones. For a single (SE), recent developments lead to theestablishment of existence and non-existence results for a wide range ofnatural nonlinearities in (SE) in the sub-critical, critical and super-criticalregimes. However for systems of (SE), there are still many interesting openquestions for basic nonlinearities. It certainly requires innovative ideas toshed some light to treat these complex situations. So far, only a very fewspecific nonlinearities have been addressed. Unlike the single (SE), thecorresponding strict sub-additivity inequality is challenging and an improvedconcentration-compactness theorem is critical to treat (NGSS) of systems of(SE). The aim of this paper is to establish the existence of (NGSS) for a largeclass of nonlinearities. This class includes many relevant pure-power typenonlinearities and can be easily extended to Hartree type nonlinearities (and acombination of both). The presence of the fractional Laplacian adds aconsiderable difficulty to rule out the dichotomy. We were able to overcomethis challenge and establish very general assumptions ensuring the strictsubadditivity of the constrained energy functional. We believe that ourapproach will open the door to many unresolved problems.

Normalized Ground State Solutions for Fractional Schrodinger Systems with General Nonlinearities