| Title: | Concentrating solutions of the fractional $(p,q)$-Choquard equation with exponential growth |
|---|
| Authors: | ID Song, Yueqiang (Author)
ID Sun, Xueqi (Author)
ID Repovš, Dušan (Author) |
|---|
| Files: |  PDF - Presentation file, download (500,70 KB)
MD5: 4772BB1F2D625A20A59555D61184431F
 URL - Source URL, visit https://www.worldscientific.com/doi/epdf/10.1142/S0219530525500290
|
|---|
| Language: | English |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
|
|---|
| Abstract: | 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. |
|---|
| Keywords: | fractional double phase operator, critical exponential growth, mountain pass theorem, Trudinger–Moser inequality, variational method |
|---|
| Publication status: | Published |
|---|
| Publication version: | Author Accepted Manuscript |
|---|
| Publication date: | 01.01.2026 |
|---|
| Year of publishing: | 2026 |
|---|
| Number of pages: | str. 665-704 |
|---|
| Numbering: | Vol. 24, iss. 3 |
|---|
| PID: | 20.500.12556/DiRROS-28044  |
|---|
| UDC: | 517.9 |
|---|
| ISSN on article: | 0219-5305 |
|---|
| DOI: | 10.1142/S0219530525500290 |
|---|
| COBISS.SI-ID: | 237989123 |
|---|
| Note: |
|
|---|
| Publication date in DiRROS: | 09.03.2026 |
|---|
| Views: | 168 |
|---|
| Downloads: | 109 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
