Positive solutions for singular double phase problems

Papageorgiou, Nikolaos S. (author), Repovš, Dušan (author), Vetro, Calogero (author)

We study the existence of positive solutions for a class of double phase Dirichlet equations which have the combined effects of a singular term and of a parametric superlinear term. The differential operator of the equation is the sum of a $p$-Laplacian and of a weighted $q$-Laplacian $(q<p)$ with discontinuous weight. Using the Nehari method, we show that for all small values of the parameter $\lambda > 0$, the equation has at least two positive solutions.

• Language: English
• Keywords: double phase problem, singular term, Nehari manifold, positive solutions, discontinuous weight
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2021
• Number of pages: art. 123896 (13 str.)
• Numbering: Vol. 501, ǂiss.ǂ1
• PID: 20.500.12556/RUL-128542
• UDC: 517.956.2
• ISSN on article: 0022-247X
• DOI: 10.1016/j.jmaa.2020.123896
• COBISS.SI-ID: 18898521
• Publication date in RUL: 19.07.2021

PAPAGEORGIOU, Nikolaos S., REPOVŠ, Dušan and VETRO, Calogero, 2021, Positive solutions for singular double phase problems. Journal of mathematical analysis and applications [online]. 2021. Vol. 501, no. 1. [Accessed 16 April 2025]. DOI 10.1016/j.jmaa.2020.123896. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=128542

Record is a part of a journal

• Title: Journal of mathematical analysis and applications
• Shortened title: J. math. anal. appl.
• Publisher: Elsevier
• ISSN: 0022-247X
• COBISS.SI-ID: 3081231