Pairs of positive solutions for resonant singular equations with the ▫$p$▫-Laplacian

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

We consider a nonlinear elliptic equation driven by the Dirichlet ▫$p$▫-Laplacian with a singular term and a ▫$(p-1)$▫-linear perturbation which is resonant at ▫$+\infty$▫ with respect to the principal eigenvalue. Using variational tools, together with suitable truncation and comparison techniques, we show the existence of at least two positive smooth solutions.

• Language: English
• Keywords: singular reaction, resonance, regularity, positive solutions, maximum principle, mountain pass theorem
• 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. 1-13
• Numbering: Vol. 2017, no. 249
• PID: 20.500.12556/RUL-110326
• UDC: 517.956.2
• ISSN on article: 1072-6691
• COBISS.SI-ID: 18154073
• Publication date in RUL: 13.09.2019

Record is a part of a journal

• Title: Electronic journal of differential equations
• Shortened title: Electr. j. differ. equ.
• Publisher: Southwest Texas State University, University of North Texas
• ISSN: 1072-6691
• COBISS.SI-ID: 7027289