{"title":"Further applications of the Nehari manifold method to functionals in C1(X∖{0})","authors":"Edir Júnior Ferreira Leite , Humberto Ramos Quoirin , Kaye Silva","doi":"10.1016/j.na.2025.113890","DOIUrl":null,"url":null,"abstract":"<div><div>We proceed with the study of the Nehari manifold method for functionals in <span><math><mrow><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>X</mi><mo>∖</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>X</mi></math></span> is a Banach space. We deal now with functionals whose fibering maps have two critical points (a minimizer followed by a maximizer). Under some additional conditions we show that the Nehari manifold method provides us with the ground state level and two sequences of critical values for these functionals. These results are applied to the class of <em>prescribed energy problems</em> as well as to the concave–convex problem for the <em>affine</em> <span><math><mi>p</mi></math></span>-Laplacian operator.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113890"},"PeriodicalIF":1.3000,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X25001440","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We proceed with the study of the Nehari manifold method for functionals in , where is a Banach space. We deal now with functionals whose fibering maps have two critical points (a minimizer followed by a maximizer). Under some additional conditions we show that the Nehari manifold method provides us with the ground state level and two sequences of critical values for these functionals. These results are applied to the class of prescribed energy problems as well as to the concave–convex problem for the affine -Laplacian operator.
期刊介绍:
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