{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T00:53:38Z","timestamp":1776214418269,"version":"3.50.1"},"reference-count":28,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2020,9,30]],"date-time":"2020-09-30T00:00:00Z","timestamp":1601424000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["307358\/2015-1"],"award-info":[{"award-number":["307358\/2015-1"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2016\/50453-0"],"award-info":[{"award-number":["2016\/50453-0"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/MAT\/04459\/2020"],"award-info":[{"award-number":["UIDB\/MAT\/04459\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/MAT\/04561\/2013"],"award-info":[{"award-number":["UID\/MAT\/04561\/2013"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["PTDC\/MAT-PUR\/28686\/2017"],"award-info":[{"award-number":["PTDC\/MAT-PUR\/28686\/2017"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,2,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We consider nonlinear 2nd-order elliptic problems of the type $$\\begin{align*} &amp; -\\Delta u=f(u)\\ \\textrm{in}\\ \\Omega, \\qquad u=0\\ \\textrm{on}\\ \\partial \\Omega, \\end{align*}$$where $\\Omega $ is an open $C^{1,1}$\u2013domain in ${{\\mathbb{R}}}^N$, $N\\geq 2$, under some general assumptions on the nonlinearity that include the case of a sublinear pure power $f(s)=|s|^{p-1}s$ with $0&amp;lt;p&amp;lt;1$ and of Allen\u2013Cahn type $f(s)=\\lambda (s-|s|^{p-1}s)$ with $p&amp;gt;1$ and $\\lambda&amp;gt;\\lambda _2(\\Omega )$ (the second Dirichlet eigenvalue of the Laplacian). We prove the existence of a least energy nodal (i.e., sign changing) solution and of a nodal solution of mountain-pass type. We then give explicit examples of domains where the associated levels do not coincide. For the case where $\\Omega $ is a ball or annulus and $f$ is of class $C^1$, we prove instead that the levels coincide and that least energy nodal solutions are nonradial but axially symmetric functions. Finally, we provide stronger results for the Allen\u2013Cahn type nonlinearities in case $\\Omega $ is either a ball or a square. In particular, we give a complete description of the solution set for $\\lambda \\sim \\lambda _2(\\Omega )$, computing the Morse index of the solutions.<\/jats:p>","DOI":"10.1093\/imrn\/rnaa233","type":"journal-article","created":{"date-parts":[[2020,8,14]],"date-time":"2020-08-14T10:45:30Z","timestamp":1597401930000},"page":"3760-3804","source":"Crossref","is-referenced-by-count":4,"title":["Nodal Solutions for Sublinear-Type Problems with Dirichlet Boundary Conditions"],"prefix":"10.1093","volume":"2022","author":[{"given":"Denis","family":"Bonheure","sequence":"first","affiliation":[{"name":"Universit\u00e9 libre de Bruxelles D\u00e9partement de Math\u00e9matique, , CP 214, Boulevard du Triomphe, B-1050 Bruxelles,","place":["Belgium"]}]},{"given":"Ederson","family":"Moreira dos Santos","sequence":"additional","affiliation":[{"name":"Instituto de Ci\u00eancias Matem\u00e1ticas e de Computa\u00e7\u00e3o , Universidade de S\u00e3o Paulo, Caixa Postal 668, CEP 13560-970 S\u00e3o Carlos,","place":["Brazil"]}]},{"given":"Enea","family":"Parini","sequence":"additional","affiliation":[{"name":"Aix-Marseille Universit\u00e9 , CNRS, Centrale Marseille, I2M, UMR 7373, 39 Rue Frederic Joliot Curie, 13453 Marseille,","place":["France"]}]},{"given":"Hugo","family":"Tavares","sequence":"additional","affiliation":[{"name":"Universit\u00e9 libre de Bruxelles D\u00e9partement de Math\u00e9matique, , CP 214, Boulevard du Triomphe, B-1050 Bruxelles,","place":["Belgium"]},{"name":"Instituto Superior T\u00e9cnico CAMGSD and Mathematics Department, , Universidade de Lisboa Av. Rovisco Pais, 1049-001 Lisboa,","place":["Portugal"]}]},{"given":"Tobias","family":"Weth","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Mathematik Goethe-Universit\u00e4t Frankfurt, , Robert-Mayer-Str. 10, D-60629 Frankfurt,","place":["Germany"]}]}],"member":"286","published-online":{"date-parts":[[2020,9,30]]},"reference":[{"issue":"5","key":"2026041420031951300_ref1","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.crma.2004.07.004","article-title":"Qualitative properties of nodal solutions of semilinear elliptic equations in radially symmetric domains","volume":"339","author":"Aftalion","year":"2004","journal-title":"C. R. Math. Acad. Sci. Paris"},{"issue":"4","key":"2026041420031951300_ref2","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1007\/s002090050492","article-title":"On the Morse indices of sign changing solutions of nonlinear elliptic problems","volume":"233","author":"Bartsch","year":"2000","journal-title":"Math. 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Math."},{"issue":"3","key":"2026041420031951300_ref6","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/BF00953069","article-title":"Infinitely many radial solutions of a semilinear elliptic problem on $\\textbf{R}^N$","volume":"124","author":"Bartsch","year":"1993","journal-title":"Arch. Rational Mech. Anal."},{"issue":"1","key":"2026041420031951300_ref7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0022-1236(81)90069-0","article-title":"Le nombre de solutions de certains probl\u00e8mes semi-lin\u00e9aires elliptiques","volume":"40","author":"Berestycki","year":"1981","journal-title":"J. Funct. Anal."},{"issue":"4","key":"2026041420031951300_ref8","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1512\/iumj.1979.28.28047","article-title":"Nonlinear problems with exactly three solutions","volume":"28","author":"Berger","year":"1979","journal-title":"Indiana Univ. Math. 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