Nonlocal ▫$p$▫-Kirchhoff equations with singular and critical nonlinearity termsGhanmi, Abdeljabbar (Avtor) Kratou, Mouna (Avtor) Saoudi, Kamel (Avtor) Repovš, Dušan (Avtor) Kirchhoff problemnonlocal operatorvariational methodssingular nonlinearitymultiplicity resultsThe 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.20232022-12-20 13:21:12Članek v reviji143425UDK: 517.956ISSN pri članku: 0921-7134DOI: 10.3233/ASY-221769COBISS_ID: 106559235sl