{"title":"局部 Lipschitz 函数的最小定理及其应用","authors":"Marcelo F. Furtado, João Pablo P. Da Silva","doi":"10.1007/s11854-024-0346-z","DOIUrl":null,"url":null,"abstract":"<p>We prove an abstract theorem which provides multiple critical points for locally Lipschtiz functionals under the presence of symmetry. The abstract result is applied to find multiple solutions in <i>H</i><span>\n<sup>1</sup><sub>0</sub>\n</span> (Ω) for the critical semi-linear elliptic equation − Δ<i>u</i> = <i>f</i>(<i>x, u</i>) + ∣<i>u</i>∣<sup>4/(<i>N</i>−2)</sup><i>u</i>, where <i>f</i> is a discontinuous perturbation and Ω ⊂ ℝ<sup><i>N</i></sup> is a bounded smooth domain.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A minimax theorem for locally Lipschitz functionals and applications\",\"authors\":\"Marcelo F. Furtado, João Pablo P. Da Silva\",\"doi\":\"10.1007/s11854-024-0346-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove an abstract theorem which provides multiple critical points for locally Lipschtiz functionals under the presence of symmetry. The abstract result is applied to find multiple solutions in <i>H</i><span>\\n<sup>1</sup><sub>0</sub>\\n</span> (Ω) for the critical semi-linear elliptic equation − Δ<i>u</i> = <i>f</i>(<i>x, u</i>) + ∣<i>u</i>∣<sup>4/(<i>N</i>−2)</sup><i>u</i>, where <i>f</i> is a discontinuous perturbation and Ω ⊂ ℝ<sup><i>N</i></sup> is a bounded smooth domain.</p>\",\"PeriodicalId\":502135,\"journal\":{\"name\":\"Journal d'Analyse Mathématique\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal d'Analyse Mathématique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s11854-024-0346-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal d'Analyse Mathématique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11854-024-0346-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A minimax theorem for locally Lipschitz functionals and applications
We prove an abstract theorem which provides multiple critical points for locally Lipschtiz functionals under the presence of symmetry. The abstract result is applied to find multiple solutions in H10 (Ω) for the critical semi-linear elliptic equation − Δu = f(x, u) + ∣u∣4/(N−2)u, where f is a discontinuous perturbation and Ω ⊂ ℝN is a bounded smooth domain.
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