Positive solutions for the Robin p-Laplacian plus an indefinite potential

Nikolaos Socrates Papageorgiou (Author), Vicenţiu Rǎdulescu (Author), Dušan Repovš (Author)

Abstract

We consider a nonlinear elliptic equation driven by the Robin ▫$p$▫-Laplacian plus an indefinite potential. In the reaction we have the competing effects of a strictly ▫$(p-1)$▫-sublinear parametric term and of a ▫$(p-1)$▫-linear and nonuniformly nonresonant term. We study the set of positive solutions as the parameter ▫$\lambda > 0$▫ varies. We prove a bifurcation-type result for large values of the positive parameter ▫$\lambda$▫. Also, we show that for all admissible ▫$\lambda > 0$▫, the problem has a smallest positive solution ▫$\overline{u}_\lambda$▫ and we study the monotonicity and continuity properties of the map ▫$\lambda \mapsto \overline{u}_\lambda$▫.

Keywords

local minimizers;p-Laplacian;strong comparison;positive solutions;nonlinear regularity;minimal solution;indefinite potential;

Data

Language:	English
Year of publishing:	2020
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	517.956
COBISS:	32039427
ISSN:	2189-3756
Views:	297
Downloads:	45
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	str. 1217-1236
Volume:	ǂVol. ǂ5
Issue:	ǂno. ǂ15
Chronology:	2020
ID:	12072181