Concentrating solutions of the fractional $(p,q)$-Choquard equation with exponential growth

Song, Yueqiang (avtor), Sun, Xueqi (avtor), Repovš, Dušan (avtor)

This paper deals with the following fractional $(p,q)$-Choquard equation with exponential growth of the form: $\varepsilon^{p s} (-\Delta)^{s}_{p} u + \varepsilon^{q s} (-\Delta)^{s}_{q} u + Z(x) ( |u|^{p-2} u + |u|^{q-2} u)$ $=\varepsilon^{\mu - N} [ |x|^{-\mu} * F(u) ] f(u)$ in $\mathbb{R}^N,$ where $s \in (0,1)$, $\varepsilon > 0$ is a parameter, $2 \leq p = \frac{N}{s} < q$, and $0 < \mu < N$. The nonlinear function $f$ has exponential growth at infinity, and the continuous potential function $Z$ satisfies suitable natural conditions. Using Ljusternik–Schnirelmann category theory and variational methods, the multiplicity and concentration of positive solutions are obtained for $\varepsilon > 0$ small enough. In a certain sense, we generalize some previously known results.

• Jezik: Angleški jezik
• Ključne besede: fractional double phase operator, critical exponential growth, mountain pass theorem, Trudinger–Moser inequality, variational method
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko ; PEF - Pedagoška fakulteta
• Status publikacije: Objavljeno
• Različica publikacije: Recenzirani rokopis
• Datum objave: 01.01.2026
• Leto izida: 2026
• Št. strani: Str. 665-704
• Številčenje: Vol. 24, iss. 3
• PID: 20.500.12556/RUL-180410
• UDK: 517.9
• ISSN pri članku: 0219-5305
• DOI: 10.1142/S0219530525500290
• COBISS.SI-ID: 237989123
• Datum objave v RUL: 09.03.2026

Gradivo je del revije

• Naslov: Analysis and applications
• Založnik: World Scientific
• ISSN: 0219-5305
• COBISS.SI-ID: 15054425

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.