{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T05:28:01Z","timestamp":1769750881780,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,8,24]],"date-time":"2021-08-24T00:00:00Z","timestamp":1629763200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We consider a nonlinear Dirichlet problem driven by the double phase differential operator and with a superlinear reaction which need not satisfy the Ambrosetti\u2013Rabinowitz condition. Using the Nehari manifold, we show that the problem has at least three nontrivial bounded solutions: nodal, positive and by the symmetry of the behaviour at +\u221e and \u2212\u221e also negative.<\/jats:p>","DOI":"10.3390\/sym13091556","type":"journal-article","created":{"date-parts":[[2021,8,24]],"date-time":"2021-08-24T22:09:39Z","timestamp":1629842979000},"page":"1556","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Multiplicity Theorem for Superlinear Double Phase Problems"],"prefix":"10.3390","volume":"13","author":[{"given":"Beata","family":"Der\u0229gowska","sequence":"first","affiliation":[{"name":"Department of Mathematics, Pedagogical University of Cracow, Podchorazych 2, 30-084 Cracow, Poland"}]},{"given":"Leszek","family":"Gasi\u0144ski","sequence":"additional","affiliation":[{"name":"State Higher Vocational School in Tarnow, Institute of Mathematical and Natural Science, Mickiewicza 8, 33-100 Tarnow, Poland"}]},{"given":"Nikolaos S.","family":"Papageorgiou","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Technical University, Zografou Campus, 15780 Athens, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"125197","DOI":"10.1016\/j.jmaa.2021.125197","article-title":"Recent developments in problems with nonstandard growth and nonuniform ellipticity","volume":"501","author":"Mingione","year":"2021","journal-title":"J. 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