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

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

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.

• Language: English
• Keywords: fractional double phase operator, critical exponential growth, mountain pass theorem, Trudinger–Moser inequality, variational method
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics; PEF - Faculty of Education
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Publication date: 01.01.2026
• Year: 2026
• Number of pages: Str. 665-704
• Numbering: Vol. 24, iss. 3
• PID: 20.500.12556/RUL-180410
• UDC: 517.9
• ISSN on article: 0219-5305
• DOI: 10.1142/S0219530525500290
• COBISS.SI-ID: 237989123
• Publication date in RUL: 09.03.2026

Record is a part of a journal

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

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.