Nonlocal $p$-Kirchhoff equations with singular and critical nonlinearity terms

Ghanmi, Abdeljabbar (avtor), Kratou, Mouna (avtor), Saoudi, Kamel (avtor), Repovš, Dušan (avtor)

The objective of this work is to investigate a nonlocal problem involving singular and critical nonlinearities: $$\begin{cases} ([u]_{s,p}^p)^{\sigma-1}(-\Delta)^s_p u = \frac{\lambda}{u^{\gamma}}+u^{ p_s^{*}-1} & \quad \text{in }\Omega,\\ u>0, & \quad \text{in }\Omega,\\ u=0, & \quad \text{in }\mathbb{R}^{N}\setminus \Omega, \end{cases}$$ where $\Omega$ is a bounded domain in $\mathbb{R}^N$ with the smooth boundary $\partial \Omega$, $0 < s< 1<p<\infty$, $N> sp$, $1<\sigma<p^*_s/p,$ with $p_s^{*}=\frac{Np}{N-ps},$ $(- \Delta )_p^s$ is the nonlocal $p$-Laplace operator and $[u]_{s,p}$ is the Gagliardo $p$-seminorm. We combine some variational techniques with a truncation argument in order to show the existence and the multiplicity of positive solutions to the above problem.

• Jezik: Angleški jezik
• Ključne besede: Kirchhoff problem, nonlocal operator, variational methods, singular nonlinearity, multiplicity results
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Različica publikacije: Recenzirani rokopis
• Leto izida: 2023
• Št. strani: Str. 125-143
• Številčenje: Vol. 131, iss. 1
• PID: 20.500.12556/RUL-143425
• UDK: 517.956
• ISSN pri članku: 0921-7134
• DOI: 10.3233/ASY-221769
• COBISS.SI-ID: 106559235
• Datum objave v RUL: 20.12.2022

GHANMI, Abdeljabbar, KRATOU, Mouna, SAOUDI, Kamel in REPOVŠ, Dušan, 2023, Nonlocal ▫$p$▫-Kirchhoff equations with singular and critical nonlinearity terms. Asymptotic analysis [na spletu]. 2023. Vol. 131, no. 1, p. 125–143. [Dostopano 14 marec 2025]. DOI 10.3233/ASY-221769. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=143425

Gradivo je del revije

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