20.500.12556/RUL-143425 Nonlocal ▫$p$▫-Kirchhoff equations with singular and critical nonlinearity terms 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. Kirchhoff problem nonlocal operator variational methods singular nonlinearity multiplicity results true false false Angleški jezik Ni določen Članek v reviji 2022-12-20 13:21:12 2022-12-20 13:21:15 2022-12-21 03:36:53 0000-00-00 00:00:00 2023 0 0 Str. 125-143 iss. 1 Vol. 131 2023 0000-00-00 PostprintKoncna NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.956 0921-7134 10.3233/ASY-221769 106559235 RAZ_Ghanmi_Abdeljabbar_2023.pdf RAZ_Ghanmi_Abdeljabbar_2023.pdf 1 1E4F2A3EFE1D49D631D666285DBF9C52 8722646329995bf480bcc2bdcb238e0558c460c53f2301988b2598558beecea5 fea0e7b9-8060-11ed-9c94-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=165117 https://content.iospress.com/articles/asymptotic-analysis/asy221769 1 a03dbed8-8060-11ed-9c94-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=165116 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0