Geodesic
Multiplicity and concentration of solutions to a fractional p-Laplace problem with exponential growth
Nguyen Van Thin1
1Thai 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

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  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 
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
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