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

In this paper, we consider minimization problems related to the combinedpower-type nonlinear scalar field equations involving the Sobolev criticalexponent in three space dimensions. In four and higher space dimensions, it isknown that for any frequency and any power of the subcritical nonlinearity,there exists a ground state. In contrast to those cases, when the spacedimension is three and the subcritical power is three or less, we can show thatthere exists a threshold frequency, above which no ground state exists, andbelow which the ground state exists. Furthermore, we prove the differencebetween two typical variational problems used to characterize the groundstates.

Non-existence of ground states and gap of variational problems for  combined power-type nonlinear scalar field equations involving the Sobolev  critical exponent in three space dimensions