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

In this paper the question of finding infinitely many solutions to theproblem $-\Delta u+a(x)u=|u|^{p-2}u$, in $\mathbb{R}^N$, $u \inH^1(\mathbb{R}^N)$, is considered when $N\geq 2$, $p \in (2, 2N/(N-2))$, andthe potential $a(x)$ is a positive function which is not required to enjoysymmetry properties. Assuming that $a(x)$ satisfies a suitable "slow decay atinfinity" condition and, moreover, that its graph has some "dips", we provethat the problem admits either infinitely many nodal solutions eitherinfinitely many constant sign solutions. The proof method is purely variationaland allows to describe the shape of the solutions.

Multiple Solutions for Scalar Field Equations with Potentials having "Subsidences"