Geodesic
Multiplicity and concentration of solutions to a fractional p-Laplace problem with exponential growth
Nguyen Van Thin1
1 Thai Nguyen University of Education, Department of Mathematics, and Thang Long University, Thang Long Institute of Mathematics and Applied Sciences
Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 603-639.

Voir la notice de l'article provenant de la source Journal.fi

  In this paper, we study the Schrödinger equation involving $\frac{N}{s}$-fractional Laplace as follows $\varepsilon^{N}(-\Delta)_{N/s}^{s}u+V(x)|u|^{\frac{N}{s}-2}u=f(u)$ in $\mathbb R^{N}$, where $\varepsilon$ is a positive parameter, $N=ps$, $s\in (0,1)$. The nonlinear function $f$ has the exponential growth and potential function $V$ is a continuous function satisfying some suitable conditions. Our problem lacks of compactness. By using the Ljusternik-Schnirelmann theory, we obtain the existence, multiplicity and concentration of nontrivial nonnegative solutions for small values of the parameter.  
DOI : 10.54330/afm.115564
Keywords: Critical exponential growth, fractional p-Laplace, Ljusternik-Schnirelmann theory, Mountain Pass Theorem, Trudinger-Moser inequality, variational method

Nguyen Van Thin 1

1 Thai Nguyen University of Education, Department of Mathematics, and Thang Long University, Thang Long Institute of Mathematics and Applied Sciences 
@article{AFM_2022_47_2_a0,
     author = {Nguyen Van Thin},
     title = {Multiplicity and concentration of solutions to a fractional {p-Laplace} problem with exponential growth},
     journal = {Annales Fennici Mathematici},
     pages = {603--639},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2022},
     doi = {10.54330/afm.115564},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.54330/afm.115564/}
}
TY  - JOUR
AU  - Nguyen Van Thin
TI  - Multiplicity and concentration of solutions to a fractional p-Laplace problem with exponential growth
JO  - Annales Fennici Mathematici
PY  - 2022
SP  - 603
EP  - 639
VL  - 47
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.54330/afm.115564/
DO  - 10.54330/afm.115564
LA  - en
ID  - AFM_2022_47_2_a0
ER  - 
%0 Journal Article
%A Nguyen Van Thin
%T Multiplicity and concentration of solutions to a fractional p-Laplace problem with exponential growth
%J Annales Fennici Mathematici
%D 2022
%P 603-639
%V 47
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.54330/afm.115564/
%R 10.54330/afm.115564
%G en
%F AFM_2022_47_2_a0
Nguyen Van Thin. Multiplicity and concentration of solutions to a fractional p-Laplace problem with exponential growth. Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 603-639. doi : 10.54330/afm.115564. http://geodesic.mathdoc.fr/articles/10.54330/afm.115564/

Cité par Sources :