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

Gradivo je del revije

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