Anisotropic $(p,q)$-equations with convex and negative concave terms

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

We consider a parametric Dirichlet problem driven by the anisotropic $(p, q)$-Laplacian and with a reaction which exhibits the combined effects of a superlinear (convex) term and of a negative sublinear term. Using variational tools and critical groups we show that for all small values of the parameter, the problem has at least three nontrivial smooth solutions, two of which are of constant sign (positive and negative).

• Language: English
• Keywords: variable Lebesgue spaces, variable Sobolev spaces, variable $(p,q)$-operator, regularity theory, local minimizer, critical point theory
• Typology: 1.16 - Independent Scientific Component Part or a Chapter in a Monograph
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2023
• Number of pages: Str. 425-441
• PID: 20.500.12556/RUL-146994
• UDC: 517.9
• DOI: 10.1007/978-3-031-20021-2_21
• COBISS.SI-ID: 154485507
• Publication date in RUL: 19.06.2023

PAPAGEORGIOU, Nikolaos S., REPOVŠ, Dušan and VETRO, Calogero, 2023, Anisotropic $(p,q)$-equations with convex and negative concave terms. In : Recent advances in mathematical analysis [online]. Cham. p. 425–441. P. 425–441. [Accessed 17 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=146994

Record is a part of a monograph

• Title: Recent advances in mathematical analysis : celebrating the 70th anniversary of Francesco Altomare
• Editors: Anna Maria Candela, Mirella Cappelletti Montano, Elisabetta Mangino
• Place of publishing: Cham
• Publisher: Birkhäuser, Springer Nature
• Year: 2023
• ISBN: 978-3-031-20020-5
• COBISS.SI-ID: 154457859
• Collection title: Trends in mathematics