Multiplicity and concentration of solutions to a fractional NS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\over{S}$$\end{document}-Laplacian problem with exponential critical growth and potentials competition

By using the Ljusternik-Schnirelmann category and variational method, we study the existence, multiplicity and concentration of solutions to the fractional Schrödinger equation with potentials competition as follows εN(−Δ)N/ssu+V(x)∣u∣Ns−2u=Q(x)h(u)inRN,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon^{N}(-\Delta)_{N/s}^{s}u+V(x)|u|^{{{N}\over{s}}-2}u=Q(x)h(u)\,\,\text{in}\,\, \mathbb{R}^{N},$$\end{document} where ε > 0 is a parameter, s ∈ (0, 1), 2 ≤ p < +∞ and N = ps. The nonlinear term h is a differentiable function with exponential critical growth, the absorption potential V and the reaction potential Q are continuous functions.