20.500.12556/RUL-154014 Existence and multiplicity of solutions for critical Kirchhoff-Choquard equations involving the fractional $p$-Laplacian on the Heisenberg group In this paper, we study existence and multiplicity of solutions for the following Kirchhoff-Choquard type equation involving the fractional $p$-Laplacian on the Heisenberg group: $M(\|u\|_\mu^{p})(\mu(-\Delta)^{s}_{p}u+V(\xi)|u|^{p-2}u)= f(\xi,u)+\int_{\mathbb{H}^N}\frac{|u(\eta)|^{Q_\lambda^{\ast}}}{|\eta^{-1}\xi|^\lambda}d\eta|u|^{Q_\lambda^{\ast}-2}u$ in $\mathbb{H}^N$, where $(-\Delta)^{s}_{p}$ is the fractional $p$-Laplacian on the Heisenberg group $\mathbb{H}^N$, $M$ is the Kirchhoff function, $V(\xi)$ is the potential function, $0 < s < 1$, $1 < p < \frac{N}{s}$, $\mu > 0$, $f(\xi,u)$ is the nonlinear function, $0 < \lambda < Q$, $Q=2N+2$, and $Q_\lambda^{\ast}=\frac{2Q-\lambda}{Q-2}$ is the Sobolev critical exponent. Using the Krasnoselskii genus theorem, the existence of infinitely many solutions is obtained if $\mu$ is sufficiently large. In addition, using the fractional version of the concentrated compactness principle, we prove that problem has $m$ pairs of solutions if $\mu$ is sufficiently small. As far as we know, the results of our study are new even in the Euclidean case. fractional concentration-compactness principle Krasnoselskii genus Kirchhoff-Choquard type equations Heisenberg group true false true Angleški jezik Ni določen Za shranitev recenziranega rokopisa v Repozitorij Univerze v Ljubljani je bilo pridobljeno založnikovo dovoljenje. (Datum opombe: 19. 1. 2024) Članek v reviji 2024-01-19 08:39:41 2024-01-19 08:39:45 2024-01-20 03:43:24 0000-00-00 00:00:00 2024 0 0 Str. 143-166 no. 1 Vol. 8 2024 0000-00-00 PostprintKoncna Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.9 2560-6778 10.23952/jnva.8.2024.1.08 181483523 RRAZ_Bai_Shujie_2024.pdf RRAZ_Bai_Shujie_2024.pdf 1 2F179A6BC6A94C4C76094E3E3071AE1F e121322638a456c39a0c7f2b544138459df9beb33f070780063f32dafe7864b8 5dfa616d-b6af-11ee-b009-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=180142 https://jnva.biemdas.com/archives/2197 1 ec4c86ad-b69d-11ee-b009-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=180138 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0