Nonlinear Dirichlet problems with unilateral growth on the reaction

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

Povzetek

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

Ključne besede

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

Podatki

Jezik:	Angleški jezik
Leto izida:	2019
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	517.956.2
COBISS:	18471257
ISSN:	0933-7741
Št. ogledov:	19
Št. prenosov:	7
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Vrsta dela (COBISS):	Delo ni kategorizirano
Strani:	str. 319-340
Letnik:	ǂVol. ǂ31
Zvezek:	ǂiss. ǂ2
Čas izdaje:	2019
DOI:	10.1515/forum-2018-0114
ID:	11193866