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

Zhang, Zhongyi (avtor), Repovš, Dušan (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: fractional Schrödinger-Kirchhoff-Poisson equations, degenerate cases, concentration compactness principle, upper critical nonlinearity, variational methods
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Recenzirani rokopis
• Datum objave: 01.01.2023
• Leto izida: 2023
• Št. strani: Str. 1219-1238
• Številčenje: Vol. 68, no. 7
• PID: 20.500.12556/RUL-182452
• UDK: 517.956
• ISSN pri članku: 1747-6933
• DOI: 10.1080/17476933.2022.2040022
• COBISS.SI-ID: 99789827
• Datum objave v RUL: 12.05.2026

Gradivo je del revije

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

Licence

• Licenca: CC BY-NC 4.0, Creative Commons Priznanje avtorstva-Nekomercialno 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc/4.0/deed.sl
• Opis: Licenca Creative Commons, ki prepoveduje komercialno uporabo, vendar uporabniki ne rabijo upravljati materialnih avtorskih pravic na izpeljanih delih z enako licenco.