On a class of Kirchhoff problems via local mountain pass

Ambrosio, Vincenzo (avtor), Repovš, Dušan (avtor)

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).

• Jezik: Angleški jezik
• Ključne besede: Kirchhoff problems, penalization method, Ljusternik-Schnirelmann theory, critical growth, supercritical exponent
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2022
• Št. strani: Str. 1-43
• Številčenje: Vol. 126, iss.1-2
• PID: 20.500.12556/RUL-133972
• UDK: 517.951
• ISSN pri članku: 0921-7134
• DOI: 10.3233/ASY-201660
• COBISS.SI-ID: 43614723
• Datum objave v RUL: 21.12.2021

AMBROSIO, Vincenzo in REPOVŠ, Dušan, 2022, On a class of Kirchhoff problems via local mountain pass. Asymptotic analysis [na spletu]. 2022. Vol. 126, no. 1–2, p. 1–43. [Dostopano 22 avgust 2025]. DOI 10.3233/ASY-201660. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=133972

Gradivo je del revije

• Naslov: Asymptotic analysis
• Skrajšan naslov: Asymptot. anal.
• Založnik: IOS Press, Sage Publications
• ISSN: 0921-7134
• COBISS.SI-ID: 25030144