Double-phase problems and a discontinuity property of the spectrum

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

We consider a nonlinear eigenvalue problem driven by the sum of ▫$p$▫ and ▫$q$▫-Laplacians. We show that the problem has a continuous spectrum. Our result reveals a discontinuity property for the spectrum of a parametric ▫$(p,q)$▫-differential operator as the parameter ▫$\beta $▫ goes to ▫$1^-$▫.

• Language: English
• Keywords: Nehari manifold, continuous spectrum, nonlinear regularity theory
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2019
• Number of pages: Str. 2899-2910
• Numbering: Vol. 147, no. 7
• PID: 20.500.12556/RUL-108798
• UDC: 517.956
• ISSN on article: 0002-9939
• DOI: 10.1090/proc/14466
• COBISS.SI-ID: 18602073
• Publication date in RUL: 26.07.2019

Record is a part of a journal

• Title: Proceedings of the American Mathematical Society
• Shortened title: Proc. Am. Math. Soc.
• Publisher: American Mathematical Society
• ISSN: 0002-9939
• COBISS.SI-ID: 2335236