CONCENTRATION PHENOMENA AND COMPETITION EFFECTS FOR FRACTIONAL KIRCHHOFF-CHOQUARD EQUATIONS WITH EXPONENTIAL GROWTH

doi:10.1007/s10473-026-0208-0

Acta mathematica scientia,Series B ›› 2026, Vol. 46 ›› Issue (2): 642-696.doi: 10.1007/s10473-026-0208-0

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CONCENTRATION PHENOMENA AND COMPETITION EFFECTS FOR FRACTIONAL KIRCHHOFF-CHOQUARD EQUATIONS WITH EXPONENTIAL GROWTH

Tahir BOUDJERIOU¹, Vicenţiu D. RĂDULESCU^2,3,4,5, Thin Van NGUYEN^6,*

1. Department of Basic Teaching, Institute of Electrical & Electronic Engineering University of Boumerdes, Boumerdes, 35000, Algeria;
2. Faculty of Applied Mathematics, AGH University of Krak ów, Krak ów 30-059, Poland;
3. Brno University of Technology, Faculty of Electrical Engineering and Communication, Technick á; 3058/10, Brno 61600, Czech Republic;
4. Simion Stoilow Institute of Mathematics of the Romanian Academy, Calea Griviţei 21, 010702 Bucharest, Romania;
5. Scientiﬁc Research Center, Baku Engineering University, Baku AZ0102, Azerbaijan;
6. Department of Mathematics, Thai Nguyen University of Education, Luong Ngoc Quyen street, Phan Dinh Phung ward, Thai Nguyen, Viet Nam

Received:2024-11-20 Revised:2025-04-21 Published:2026-05-22
Contact: ^*Thin Van NGUYEN, E-mail: thinmath@gmail.com; thinnv@tnue.edu.vn
About author:Tahir BOUDJERIOU, E-mail: t.boudjeriou@univ-boumerdes.dz; Vicenţiu D. RĂDULESCU, E-mail: radulescu@inf.ucv.ro
Supported by:
The research of Thin Van Nguyen was supported by Ministry of Education and Training of Vietnam under project with the name "Existence of normalized solutions and blow up of solutions for some classes of partial differential equations containing fractional $p$-Laplace operators" and grant number B2026-TNA-02. The research of Vicenţ iu D. Ră dulescu was supported by the grant "Nonlinear Differential Systems in Applied Sciences" of the Romanian Ministry of Research, Innovation and Digitization, within PNRR-III-C9-2022-I8/22. He was also supported by the AGH University of Krakó w under grant no. 16.16.420.054, funded by the Polish Ministry of Science and Higher Education.

Abstract

Abstract: In this paper, we study the fractional Kirchhoff-Choquard equation $\begin{align*} &M\bigg([u]_{s,p}^{p}+\varepsilon^{-N}\int\limits_{\mathbb R^N}V( x)|u|^{p}{\rm d}x\bigg)(\varepsilon^{N}(-\Delta)_{p}^{s}u+V(x)|u|^{p-2}u)\\ =\,&\varepsilon^{\mu-N}\bigg(\int\limits_{\mathbb R^N}\dfrac{Q(y)F(u(y))}{|x-y|^{\mu}}{\rm d}y\bigg)Q(x)f(u(x))\quad\text{in}\; \mathbb R^{N}, \end{align*}$ where $\varepsilon$ is a positive parameter, $N=ps, p\ge 2, s\in (0,1),0<\mu<N.$ The Kirchhoff function $M(t)=a+bt, a>0,b>0$, nonlinear function $f$ has the exponential growth, potential functions $V$ and $Q$ are continuous functions satisfying some suitable conditions. Using Ljusternik-Schnirelmann category theory and variational methods, we establish the multiplicity and concentration of positive solutions for small values of the parameter.

Key words: critical exponential, fractional $p$-Laplace, Ljusternik-Schnirelmann category, Mountain Pass Theorem, Trudinger-Moser inequality, variational techniques

CLC Number:

35A15

Tahir BOUDJERIOU, Vicenţiu D. RĂDULESCU, Thin Van NGUYEN. CONCENTRATION PHENOMENA AND COMPETITION EFFECTS FOR FRACTIONAL KIRCHHOFF-CHOQUARD EQUATIONS WITH EXPONENTIAL GROWTH[J].Acta mathematica scientia,Series B, 2026, 46(2): 642-696.

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CONCENTRATION PHENOMENA AND COMPETITION EFFECTS FOR FRACTIONAL KIRCHHOFF-CHOQUARD EQUATIONS WITH EXPONENTIAL GROWTH

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