Positive solutions for nonlinear parametric singular Dirichlet problems

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

We consider a nonlinear parametric Dirichlet problem driven by the ▫$p$▫-Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Carathéodory perturbation which is ▫$p-1$▫-linear near ▫$+\infty$▫. The problem is uniformly nonresonant with respect to the principal eigenvalue of ▫$(-\Delta _p,W^{1,p}_0(\Omega ))$▫. We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter ▫$\lambda >0$▫.

• Language: English
• Keywords: parametric singular term, (p-1)-linear perturbation, uniform nonresonance, nonlinear regularity theory, truncation, strong comparison principle, bifurcation-type theorem
• 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: art. 1950011 (21 str.)
• Numbering: Vol. 9, iss. 3
• PID: 20.500.12556/RUL-109066
• UDC: 517.956.2
• ISSN on article: 1664-3607
• DOI: 10.1142/S1664360719500115
• COBISS.SI-ID: 18403929
• Publication date in RUL: 20.08.2019

Record is a part of a journal

• Title: Bulletin of mathematical sciences
• Shortened title: Bull. math. sci.
• Publisher: Springer International Publishing
• ISSN: 1664-3607
• COBISS.SI-ID: 18343257