Existence and multiplicity of solutions for resonant $(p,2)$-equations

Papageorgiou, Nikolaos S. (author), Rǎdulescu, Vicenţiu (author), Repovš, Dušan (author)

We consider Dirichlet elliptic equations driven by the sum of a $p$-Laplacian $(2 < p)$ and a Laplacian. The conditions on the reaction term imply that the problem is resonant at both $\pm \infty$ and at zero. We prove an existence theorem (producing one nontrivial smooth solution) and a multiplicity theorem (producing five nontrivial smooth solutions, four of constant sign and the fifth nodal; the solutions are ordered). Our approach uses variational methods and critical groups.

• Language: English
• Keywords: resonance, variational eigenvalues, critical groups, nonlinear regularity, multiple solutions, nodal solutions
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2018
• Number of pages: Str. 105-129
• Numbering: Vol. 18, iss. 1
• PID: 20.500.12556/RUL-109142
• UDC: 517.956.2
• ISSN on article: 1536-1365
• DOI: 10.1515/ans-2017-0009
• COBISS.SI-ID: 18001241
• Publication date in RUL: 23.08.2019

PAPAGEORGIOU, Nikolaos S., RǍDULESCU, Vicenţiu and REPOVŠ, Dušan, 2018, Existence and multiplicity of solutions for resonant ▫$(p,2)$▫-equations. Advanced nonlinear studies [online]. 2018. Vol. 18, no. 1, p. 105–129. [Accessed 14 April 2025]. DOI 10.1515/ans-2017-0009. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=109142

Record is a part of a journal

• Title: Advanced nonlinear studies
• Shortened title: Adv. nonlinear stud.
• Publisher: De Gruyter
• ISSN: 1536-1365
• COBISS.SI-ID: 15060569