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 study existence, regularity, and qualitative properties of solutions tothe system \[  -\Delta u = |v|^{q-1} v\quad \text{ in }\Omega,\qquad -\Delta v = |u|^{p-1}u\quad \text{ in }\Omega,\qquad \partial_\nu u=\partial_\nu v=0\quad \text{ on}\partial\Omega, \] with $\Omega\subset \mathbb R^N$ bounded; in this setting,all nontrivial solutions are sign changing. Our proofs use a variationalformulation in dual spaces, considering sublinear $pq< 1$ and superlinear$pq>1$ problems in the subcritical regime. In balls and annuli we show thatleast energy solutions (l.e.s.) are foliated Schwarz symmetric and, due to asymmetry-breaking phenomenon, l.e.s. are not radial functions; a key element inthe proof is a new $L^t$-norm-preserving transformation, which combines asuitable flipping with a decreasing rearrangement. This combination allows usto treat annular domains, sign-changing functions, and Neumann problems, whichare non-standard settings to use rearrangements and symmetrizations. Inparticular, we show that our transformation diminishes the (dual) energy and,as a consequence, radial l.e.s. are strictly monotone. We also study uniquecontinuation properties and simplicity of zeros. Our theorems also apply to thescalar associated model, where our approach provides new results as well asalternative proofs of known facts.

Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions