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  • On degenerate fractional Schrödinger-Kirchhoff-Poisson equations with upper critical nonlinearity and electromagnetic fields
    Zhang, Zhongyi ; Repovš, Dušan, 1954-
    This paper intends to study the following degenerate fractional Schrödinger-Kirchhoff-Poisson equations with critical nonlinearity and electromagnetic fields in ▫$\mathbb{R}^3$▫: ▫$\begin{cases} ... \varepsilon^{2s}M([u]^2_{s,A})(-\Delta)^s_Au+V(x)u+\phi u \\ \quad =k(x)|u|^{r-2}u + \left(\mathcal{I}_\mu \ast |u|^{2^\sharp_s}\right)|u|^{2^\sharp_s - 2}u, & x \in \mathbb{R}^3, \\ (-\Delta)^t \phi = u^2, & x \in \mathbb{R}^3, \end{cases}$▫ where ▫$\varepsilon > 0$▫ is a positive parameter, ▫$3/4 < s < 1$▫, ▫$0 < t < 1$▫, ▫$V$▫ is an electric potential satisfying suitable assumptions, and ▫$0 < k_\ast \le k(x) \le k^\ast$▫, ▫$\mathcal{I}_\mu (x)=|x|^{3-\mu}$▫ with ▫$0 < \mu < 3$▫, ▫$2^\sharp_s = \frac{3+\mu}{3-2s}$▫ and ▫$2 < r < 2^\sharp_s$▫. With the help of the concentration compactness principle and variational method, and together with some careful analytical skills, we prove the existence and multiplicity of solutions for the above problem as ▫$\varepsilon \to 0$▫ in degenerate cases, that is the Kirchhoff term ▫$M$▫ can vanish at zero.
    Vir: Complex variables and elliptic equations. - ISSN 1747-6933 (Vol. 68, no. 7, 2023, str. 1219-1238)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2023
    Jezik - angleški
    COBISS.SI-ID - 99789827

    Povezava(-e):

    https://www.tandfonline.com/doi/full/10.1080/17476933.2022.2040022
    DOI

vir: Complex variables and elliptic equations. - ISSN 1747-6933 (Vol. 68, no. 7, 2023, str. 1219-1238)

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