{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:10:20Z","timestamp":1760123420907,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T00:00:00Z","timestamp":1676246400000},"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 Dirichlet problem, which is a perturbation of the eigenvalue problem for the anisotropic p-Laplacian. We assume that the perturbation is (p(z)\u22121)-sublinear, and we prove an existence and nonexistence theorem for positive solutions as the parameter \u03bb moves on the positive semiaxis. We also show the existence of a smallest positive solution and determine the monotonicity and continuity properties of the minimal solution map.<\/jats:p>","DOI":"10.3390\/sym15020495","type":"journal-article","created":{"date-parts":[[2023,2,14]],"date-time":"2023-02-14T02:41:56Z","timestamp":1676342516000},"page":"495","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Existence and Nonexistence of Positive Solutions for Perturbations of the Anisotropic Eigenvalue Problem"],"prefix":"10.3390","volume":"15","author":[{"given":"Olena","family":"Andrusenko","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":"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, Zografou Campus, National Technical University, 15780 Athens, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,13]]},"reference":[{"key":"ref_1","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":"Discret. 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