Constant sign and nodal solutions for parametric anisotropic $(p, 2)$-equations

Papageorgiou, Nikolaos S. (author), Repovš, Dušan (author), Vetro, Calogero (author)

We consider an anisotropic $(p, 2)$-equation, with a parametric and superlinear reaction term. We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, four with constant sign and the fifth nodal (sign-changing). The proofs use tools from critical point theory, truncation and comparison techniques, and critical groups.

• Language: English
• Keywords: anisotropic operators, regularity theory, maximum principle, constant sign and nodal solutions, critical groups, variable exponent, electrorheological fluids
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: Str. 1059-1076
• Numbering: Vol. 102, no. 4
• PID: 20.500.12556/RUL-145164
• UDC: 517.956.2
• ISSN on article: 0003-6811
• DOI: 10.1080/00036811.2021.1971199
• COBISS.SI-ID: 76549635
• Publication date in RUL: 12.04.2023

Record is a part of a journal

• Title: Applicable analysis
• Shortened title: Appl. anal.
• Publisher: Taylor & Francis
• ISSN: 0003-6811
• COBISS.SI-ID: 24981760

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• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
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