Vincenzo Ambrosio (Avtor), Dušan Repovš (Avtor)

Povzetek

In the present work we study the multiplicity and concentration of positive solutions for the following class of Kirchhoff problems: ▫$$\begin{cases}-(\varepsilon^2a+\varepsilon b\int _{\mathbb{R}^3}|\nabla u|^2 dx) \Delta u + V(x)u = f(u)+\gamma u^5 & \text{in} \; \mathbb{R}^3, \\ u \in H^1(\mathbb{R}^3), \quad u>0 & \text{in} \; \mathbb{R}^3, \end{cases}$$▫ where ▫$\varepsilon>0$▫ is a small parameter, ▫$a,b>0$▫ are constants, ▫$\gamma \in {0,1}$▫, ▫$V$▫ is a continuous positive potential with a local minimum, and ▫$f$▫ is a superlinear continuous function with subcritical growth. The main results are obtained through suitable variational and topological arguments. We also provide a multiplicity result for a supercritical version of the above problem by combining a truncation argument with a Moser-type iteration. Our theorems extend and improve in several directions the studies made in (Adv. Nonlinear Stud. 14 (2014), 483-510; J. Differ. Equ. 252 (2012), 1813-1834; J. Differ. Equ. 253 (2012), 2314-2351).

Ključne besede

Kirchhoff problems;penalization method;Ljusternik-Schnirelmann theory;critical growth;supercritical exponent;

Podatki

Jezik: Angleški jezik
Leto izida:
Tipologija: 1.01 - Izvirni znanstveni članek
Organizacija: UL FMF - Fakulteta za matematiko in fiziko
UDK: 517.956
COBISS: 43614723 Povezava se bo odprla v novem oknu
ISSN: 0921-7134
Št. ogledov: 168
Št. prenosov: 60
Ocena: 0 (0 glasov)
Metapodatki: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Ostali podatki

Vrsta dela (COBISS): Članek v reviji
Strani: str. 1-43
Letnik: ǂVol. ǂ126
Zvezek: ǂiss. ǂ1-2
Čas izdaje: 2022
DOI: 10.3233/ASY-201660
ID: 14119068