Nonlinear nonhomogeneous Robin problems with almost critical and partially concave reaction

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

We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Carathéodory terms. One is parametric, $(p-1)$-sublinear with a partially concave nonlinearity near zero. The other is $(p-1)$-superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter $\lambda > 0$ varies.

• Language: English
• Keywords: competition phenomena, nonlinear regularity, nonlinear maximum principle, strong comparison principle, bifurcation-type result, almost critical growth
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2020
• Number of pages: Str. 1774-1803
• Numbering: Vol. 30, iss. 2
• PID: 20.500.12556/RUL-116580
• UDC: 517.956.2
• ISSN on article: 1050-6926
• DOI: 10.1007/s12220-019-00278-0
• COBISS.SI-ID: 18727769
• Publication date in RUL: 28.05.2020

PAPAGEORGIOU, Nikolaos S., REPOVŠ, Dušan and VETRO, Calogero, 2020, Nonlinear nonhomogeneous Robin problems with almost critical and partially concave reaction. The Journal of geometric analysis [online]. 2020. Vol. 30, no. 2, p. 1774–1803. [Accessed 17 April 2025]. DOI 10.1007/s12220-019-00278-0. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=116580

Record is a part of a journal

• Title: The Journal of geometric analysis
• Shortened title: J. geom. anal.
• Publisher: Springer, Mathematica Josephina
• ISSN: 1050-6926
• COBISS.SI-ID: 30685696