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

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

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.

• Language: English
• Keywords: Kirchhoff problem, nonlocal operator, variational methods, singular nonlinearity, multiplicity results
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication version: Author Accepted Manuscript
• Year: 2023
• Number of pages: Str. 125-143
• Numbering: Vol. 131, iss. 1
• PID: 20.500.12556/RUL-143425
• UDC: 517.956
• ISSN on article: 0921-7134
• DOI: 10.3233/ASY-221769
• COBISS.SI-ID: 106559235
• Publication date in RUL: 20.12.2022

Record is a part of a journal

• Title: Asymptotic analysis
• Shortened title: Asymptot. anal.
• Publisher: IOS Press
• ISSN: 0921-7134
• COBISS.SI-ID: 25030144