On degenerate fractional Schrödinger-Kirchhoff-Poisson equations with upper critical nonlinearity and electromagnetic fields

Zhang, Zhongyi (author), Repovš, Dušan (author)

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.

• Language: English
• Keywords: fractional Schrödinger-Kirchhoff-Poisson equations, degenerate cases, concentration compactness principle, upper critical nonlinearity, variational methods
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Publication date: 01.01.2023
• Year: 2023
• Number of pages: Str. 1219-1238
• Numbering: Vol. 68, no. 7
• PID: 20.500.12556/RUL-182452
• UDC: 517.956
• ISSN on article: 1747-6933
• DOI: 10.1080/17476933.2022.2040022
• COBISS.SI-ID: 99789827
• Publication date in RUL: 12.05.2026

Record is a part of a journal

• Title: Complex variables and elliptic equations
• Publisher: Taylor & Francis
• ISSN: 1747-6933
• COBISS.SI-ID: 513019929

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