VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Existence and multiplicity of solutions for critical Kirchhoff-Choquard equations involving the fractional ▫$p$▫-Laplacian on the Heisenberg group [Elektronski vir]
    Bai, Shujie ; Song, Yueqiang ; Repovš, Dušan, 1954-
    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.
    Vir: Journal of nonlinear and variational analysis [Elektronski vir]. - ISSN 2560-6778 (Vol. 8, iss. 1, 2024, str. 143-166)
    Vrsta gradiva - e-članek ; neleposlovje za odrasle
    Leto - 2024
    Jezik - angleški
    COBISS.SI-ID - 181483523

    Povezava(-e):

    https://jnva.biemdas.com/archives/2197
    Repozitorij Univerze v Ljubljani – RUL
    DOI

Vnos na polico