Nonlinear nonhomogeneous singular problems

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

Abstract

We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator with a growth of order ▫$(p-1)$▫ near ▫$+\infty$▫ and with a reaction which has the competing effects of a parametric singular term and a ▫$(p-1)$▫-superlinear perturbation which does not satisfy the usual Ambrosetti-Rabinowitz condition. Using variational tools, together with suitable truncation and strong comparison techniques, we prove a "bifurcation-type" theorem that describes the set of positive solutions as the parameter ▫$\lambda$▫ moves on the positive semiaxis. We also show that for every ▫$\lambda > 0$▫, the problem has a smallest positive solution ▫$u^\ast_\lambda$▫ and we demonstrate the monotonicity and continuity properties of the map ▫$\lambda \mapsto u^\ast_\lambda$▫.

Keywords

singular term;superlinear perturbation;positive solution;nonhomogeneous differential operator;nonlinear regularity;minimal positive solutions;strong comparison principle;

Data

Language:	English
Year of publishing:	2020
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	517.956.2
COBISS:	18823001
ISSN:	0944-2669
Views:	502
Downloads:	329
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	art. 9 [31 str.]
Volume:	ǂVol. ǂ59
Issue:	ǂiss. ǂ1
Chronology:	Feb. 2020
DOI:	10.1007/s00526-019-1667-0
ID:	11763934