On the $p$-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity

Zhao, Min (avtor), Song, Yueqiang (avtor), Repovš, Dušan (avtor)

In this article, we deal with the following $p$-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity: $ M\left([u]_{s,A}^{p}\right)(-\Delta)_{p, A}^{s} u+V(x)|u|^{p-2} u=\lambda\left(\int_\limits{\mathbb{R}^{N}} \frac{|u|^{p_{\mu, s}^{*}}}{|x-y|^{\mu}} \mathrm{d}y\right)|u|^{p_{\mu, s}^{*}-2} u+k|u|^{q-2}u,\ x \in \mathbb{R}^{N},$ where $0 < s < 1 < p$, $ps < N$, $p < q < 2p^{*}_{s,\mu}$, $0 < \mu < N$, $\lambda$ and $k$ are some positive parameters, $p^{*}_{s,\mu}=\frac{pN-p\frac{\mu}{2}}{N-ps}$ is the critical exponent with respect to the Hardy-Littlewood-Sobolev inequality, and functions $V$, $M$ satisfy the suitable conditions. By proving the compactness results using the fractional version of concentration compactness principle, we establish the existence of nontrivial solutions to this problem.

• Jezik: Angleški jezik
• Ključne besede: Hardy-Littlewood-Sobolev nonlinearity, Schrödinger-Kirchhoff equations, variational methods, electromagnetic fields
• 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: Objavljena publikacija
• Leto izida: 2024
• Št. strani: 18 str.
• Številčenje: Vol. 57, iss. 1, art. 20230124
• PID: 20.500.12556/RUL-153563
• UDK: 517.9
• ISSN pri članku: 2391-4661
• DOI: 10.1515/dema-2023-0124
• COBISS.SI-ID: 180796163
• Datum objave v RUL: 16.01.2024

Gradivo je del revije

• Naslov: Demonstratio Mathematica
• Skrajšan naslov: Demonstr. Math.
• Založnik: De Gruyter Poland
• ISSN: 2391-4661
• COBISS.SI-ID: 526342681

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.