On a class of parametric ▫$(p, 2)$▫-equations

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

We consider parametric equations driven by the sum of a ▫$p$▫-Laplacian and a Laplace operator (the so-called ▫$(p, 2)$▫-equations). We study the existence and multiplicity of solutions when the parameter ▫$\lambda > 0$▫ is near the principal eigenvalue ▫$\hat{\lambda}_1(p) > 0$▫ of ▫$(-\Delta_p,W^{1-p}_0(\Omega))$▫. We prove multiplicity results with precise sign information when the near resonance occurs from above and from below of ▫$\hat{\lambda}_1(p) > 0$▫.

• Language: English
• Keywords: near resonance, local minimizer, critical group, constant sign and nodal solutions, nonlinear maximum principle
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2017
• Number of pages: Str. 193-228
• Numbering: Vol. 75, iss. 2
• PID: 20.500.12556/RUL-109938
• UDC: 517.956.2
• ISSN on article: 0095-4616
• DOI: 10.1007/s00245-016-9330-z
• COBISS.SI-ID: 17592153
• Publication date in RUL: 10.09.2019

Record is a part of a journal

• Title: Applied mathematics and optimization
• Shortened title: Appl. math. optim.
• Publisher: Springer.
• ISSN: 0095-4616
• COBISS.SI-ID: 24984064