Multiplicity and Concentration of Solutions for Kirchhoff Equations with Exponential Growth

In this paper, we deal with fractional Formula: see text-Laplace Kirchhoff equations with exponential growth of the form Formula: see text where Formula: see text is a positive parameter, Formula: see text, Formula: see text and Formula: see text. Under some appropriate conditions for the nonlinear function Formula: see text and potential function Formula: see text, and with the help of penalization method and Lyusternik–Schnirelmann theory, we establish the existence, multiplicity and concentration of solutions. To some extent, we fill in the gaps in W. Chen and H. Pan, Multiplicity and concentration of solutions for a fractional [Formula: see text-Kirchhoff type equation, Discrete Contin. Dyn. Syst. 43 (2023) 2576–2607; G. Figueiredo and J. Santos, Multiplicity and concentration behavior of positive solutions for a Schrödinger–Kirchhoff type problem via penalization method, ESAIM Control Optim. Calc. Var. 20 (2014) 389–415; X. He and W. Zou, Existence and concentration behavior of positive solutions for a Kirchhoff equation in Formula: see text J. Differential Equations 252 (2012) 1813–1834; J. Wang, L. Tian, J. Xu and F. Zhang, Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth, J. Differential Equations 253 (2012) 2314–2351].