Robin double-phase problems with singular and superlinear terms

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

We consider a nonlinear Robin problem driven by the sum of ▫$p$▫-Laplacian and ▫$q$▫-Laplacian (i.e. the ▫$p, q)$▫-equation). In the reaction there are competing effects of a singular term and a parametric perturbation ▫$\lambda f(z,x)$▫, which is Carathéodory and ▫$(p-1)$▫-superlinear at ▫$x \in \mathbb{R}$▫ without satisfying the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques, we prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter ▫$\lambda > 0$▫ varies.

• Language: English
• Keywords: nonhomogeneous differential operator, nonlinear regularity theory, truncation, strong comparison principle, positive solutions
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2021
• Number of pages: art. 103217 (20 str.)
• Numbering: Vol. 58
• PID: 20.500.12556/RUL-121291
• UDC: 517.956
• ISSN on article: 1468-1218
• DOI: 10.1016/j.nonrwa.2020.103217
• COBISS.SI-ID: 30724867
• Publication date in RUL: 02.10.2020

Record is a part of a journal

• Title: Nonlinear analysis: real world applications
• Shortened title: Nonlinear anal.: real world appl.
• Publisher: Pergamon
• ISSN: 1468-1218
• COBISS.SI-ID: 10725465