{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T09:03:31Z","timestamp":1765357411384},"reference-count":40,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T00:00:00Z","timestamp":1688947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,1,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We study the following Lane\u2013Emden system: $$\\begin{align*} &amp; -\\Delta u=|v|^{q-1}v \\quad \\ \\textrm{in}\\ \\Omega, \\qquad -\\Delta v=|u|^{p-1}u \\quad \\ \\textrm{in}\\ \\Omega, \\qquad u_{\\nu}=v_{\\nu}=0 \\quad \\ \\textrm{on}\\ \\partial \\Omega, \\end{align*}$$with $\\Omega $ a bounded regular domain of ${\\mathbb{R}}^{N}$, $N \\ge 4$, and exponents $p, q$ belonging to the so-called critical hyperbola $1\/(p+1)+1\/(q+1)=(N-2)\/N$. We show that, under suitable conditions on $p, q$, least-energy (sign-changing) solutions exist, and they are classical. In the proof we exploit a dual variational formulation, which allows to deal with the strong indefinite character of the problem. We establish a compactness condition which is based on a new Cherrier-type inequality. We then prove such condition by using as test functions the solutions to the system in the whole space and performing delicate asymptotic estimates. If $N \\ge 5$, $p=1$, the system above reduces to a biharmonic equation, for which we also prove existence of least-energy solutions. Finally, we prove some partial symmetry and symmetry-breaking results in the case $\\Omega $ is a ball or an annulus.<\/jats:p>","DOI":"10.1093\/imrn\/rnad145","type":"journal-article","created":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T09:30:58Z","timestamp":1688981458000},"page":"745-803","source":"Crossref","is-referenced-by-count":4,"title":["Existence of Solutions on the Critical Hyperbola for a Pure Lane\u2013Emden System with Neumann Boundary Conditions"],"prefix":"10.1093","volume":"2024","author":[{"given":"Angela","family":"Pistoia","sequence":"first","affiliation":[{"name":"Dipartimento di Scienze di Base e Applicate per l\u2019Ingegneria , Sapienza Universit\u00e0 di Roma, Via Scarpa 16, 00161 Roma, Italy"}]},{"given":"Delia","family":"Schiera","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico , Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]},{"given":"Hugo","family":"Tavares","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico , Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]}],"member":"286","published-online":{"date-parts":[[2023,7,10]]},"reference":[{"key":"2024010905434424700_ref1","volume-title":"Sobolev Spaces","author":"Adams","year":"2003"},{"key":"2024010905434424700_ref2","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1002\/cpa.3160120405","article-title":"Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I","volume":"12","author":"Agmon","year":"1959","journal-title":"Comm. Pure Appl. 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