{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:47:46Z","timestamp":1772293666520,"version":"3.50.1"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Eur. Math. Soc."],"published-print":{"date-parts":[[2012,6,3]]},"abstract":"<jats:p>In the recent literature, the phenomenon of phase separation for binary mixtures of Bose\u2013Einstein condensates can be understood, from a mathematical point of view, as governed by the asymptotic limit of the stationary Gross\u2013Pitaevskii system<\/jats:p>\n                  <jats:p>\n                    <jats:disp-formula>\n                      <jats:tex-math>\\left\\{ \\begin{array}{l} -\\Delta u + u^3+\\beta uv^2=\\lambda u,\\\\ -\\Delta v + v^3+\\beta u^2v=\\mu v,\\\\ u,v\\in H^1_0 (\\Omega),\\quad u,v&gt;0,\\\\ \\end{array} \\right.<\/jats:tex-math>\n                    <\/jats:disp-formula>\n                  <\/jats:p>\n                  <jats:p>\n                    as the interspecies scattering length\n                    <jats:inline-formula>\n                      <jats:tex-math>\\beta<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    goes to\n                    <jats:inline-formula>\n                      <jats:tex-math>+\\infty<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . For this system we consider the associated energy functionals\n                    <jats:inline-formula>\n                      <jats:tex-math>J_\\beta<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ,\n                    <jats:inline-formula>\n                      <jats:tex-math>\\beta\\in(0,+\\infty)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , with\n                    <jats:inline-formula>\n                      <jats:tex-math>L^2<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -mass constraints, which limit\n                    <jats:inline-formula>\n                      <jats:tex-math>J_\\infty<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    (as\n                    <jats:inline-formula>\n                      <jats:tex-math>\\beta\\to+\\infty<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ) is strongly irregular. For such functionals, we construct multiple critical points via a common minimax structure, and prove convergence of critical levels and optimal sets. Moreover we study the asymptotics of the critical points.\n                  <\/jats:p>","DOI":"10.4171\/jems\/332","type":"journal-article","created":{"date-parts":[[2012,6,6]],"date-time":"2012-06-06T18:01:13Z","timestamp":1339005673000},"page":"1245-1273","source":"Crossref","is-referenced-by-count":33,"title":["Convergence of minimax structures and continuation of critical points for singularly perturbed systems"],"prefix":"10.4171","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7941-4748","authenticated-orcid":false,"given":"Benedetta","family":"Noris","sequence":"first","affiliation":[{"name":"Universit\u00e0 degli Studi di Milano-Bicocca, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1435-7695","authenticated-orcid":false,"given":"Hugo","family":"Tavares","sequence":"additional","affiliation":[{"name":"IST - Universidade de Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6846-7841","authenticated-orcid":false,"given":"Susanna","family":"Terracini","sequence":"additional","affiliation":[{"name":"Universit\u00e0 di Torino, Italy"}]},{"given":"Gianmaria","family":"Verzini","sequence":"additional","affiliation":[{"name":"Politecnico di Milano, Italy"}]}],"member":"2673","container-title":["Journal of the European Mathematical Society"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/JEMS\/332","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T13:59:13Z","timestamp":1762869553000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/jems\/332"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,3]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.4171\/jems\/332","relation":{},"ISSN":["1435-9855","1435-9863"],"issn-type":[{"value":"1435-9855","type":"print"},{"value":"1435-9863","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,3]]}}}