Nonlinear Dirichlet problems with unilateral growth on the reaction

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

Abstract

We consider a nonlinear Dirichlet problem driven by the ▫$p$▫-Laplace differential operator with a reaction which has a subcritical growth restriction only from above. We prove two multiplicity theorems producing three nontrivial solutions, two of constant sign and the third nodal. The two multiplicity theorems differ on the geometry near the origin. In the semilinear case (that is, ▫$p=2$▫), using Morse theory (critical groups), we produce a second nodal solution for a total of four nontrivial solutions. As an illustration, we show that our results incorporate and significantly extend the multiplicity results existing for a class of parametric, coercive Dirichlet problems

Keywords

unilateral growth;constant sign and nodal solutions;multiplicity theorems;critical groups;

Data

Language:	English
Year of publishing:	2019
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	517.956.2
COBISS:	18471257
ISSN:	0933-7741
Views:	19
Downloads:	7
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Type (COBISS):	Not categorized
Pages:	str. 319-340
Volume:	ǂVol. ǂ31
Issue:	ǂiss. ǂ2
Chronology:	2019
DOI:	10.1515/forum-2018-0114
ID:	11193866