{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T01:01:02Z","timestamp":1773450062019,"version":"3.50.1"},"reference-count":11,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,30]],"date-time":"2022-01-30T00:00:00Z","timestamp":1643500800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We consider a nonlinear eigenvalue problem driven by the Dirichlet (p,2)-Laplacian. The parametric reaction is a Carath\u00e9odory function which exhibits (p\u22121)-sublinear growth as x\u2192+\u221e and as x\u21920+. Using variational tools and truncation and comparison techniques, we prove a bifurcation-type theorem describing the \u201cspectrum\u201d as \u03bb&gt;0 varies. We also prove the existence of a smallest positive eigenfunction for every eigenvalue. Finally, we indicate how the result can be extended to (p,q)-equations (q\u22602).<\/jats:p>","DOI":"10.3390\/axioms11020058","type":"journal-article","created":{"date-parts":[[2022,1,31]],"date-time":"2022-01-31T01:46:08Z","timestamp":1643593568000},"page":"58","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Nonlinear Eigenvalue Problems for the Dirichlet (p,2)-Laplacian"],"prefix":"10.3390","volume":"11","author":[{"given":"Yunru","family":"Bai","sequence":"first","affiliation":[{"name":"School of Science, Guangxi University of Science and Technology, Liuzhou 545006, China"}]},{"given":"Leszek","family":"Gasi\u0144ski","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Pedagogical University of Cracow, Podchorazych 2, 30-084 Cracow, 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":[[2022,1,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1515\/acv-2019-0040","article-title":"Constant sign and nodal solutions for superlinear double phase problems","volume":"14","author":"Papageorgiou","year":"2021","journal-title":"Adv. Calc. Var."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1515\/forum-2017-0124","article-title":"Positive solutions for nonlinear nonhomogeneous parametric Robin problems","volume":"30","author":"Papageorgiou","year":"2018","journal-title":"Forum Math."},{"key":"ref_3","first-page":"279","article-title":"Some recent results on the Dirichlet problem for (p,q)-Laplace equations","volume":"11","author":"Marano","year":"2018","journal-title":"Discrete Contin. Dyn. Syst. Ser. S"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"259","DOI":"10.7494\/OpMath.2019.39.2.259","article-title":"Isotropic and anistropic double-phase problems: Old and new","volume":"39","year":"2019","journal-title":"Opuscula Math."},{"key":"ref_5","unstructured":"Gasi\u0144ski, L., and Papageorgiou, N.S. (2006). Nonlinear Analysis, Chapman & Hall\/CRC."},{"key":"ref_6","unstructured":"Ladyzhenskaya, O.A., and Ural\u2019tseva, N.N. (1968). Linear and Quasilinear Elliptic Equations, Academic Press."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1080\/03605309108820761","article-title":"The natural generalization of the natural conditions of Ladyzhenskaya and Ural\u2019tseva for elliptic equations","volume":"16","author":"Lieberman","year":"1991","journal-title":"Comm. Partial. Differ. Equ."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Pucci, P., and Serrin, J. (2007). The Maximum Principle, Birkh\u00e4user.","DOI":"10.1007\/978-3-7643-8145-5"},{"key":"ref_9","first-page":"417","article-title":"Multiple solutions for nonlinear coercive problems with a nonhomogeneous differential operator and a nonsmooth potential","volume":"3","author":"Papageorgiou","year":"2012","journal-title":"Set-Valued Var. Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2589","DOI":"10.3934\/dcds.2017111","article-title":"Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potential","volume":"37","author":"Papageorgiou","year":"2017","journal-title":"Discrete Contin. Dyn. Syst."},{"key":"ref_11","unstructured":"Hu, S., and Papageorgiou, N.S. (1997). Handbook of Multivalued Analysis: Volume I: Theory (Mathematics and Its Applications, 419), Kluwer Academic Publishers."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/2\/58\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:11:36Z","timestamp":1760134296000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/2\/58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,30]]},"references-count":11,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["axioms11020058"],"URL":"https:\/\/doi.org\/10.3390\/axioms11020058","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,30]]}}}