Multiplicity and Concentration Behavior of Solutions to a Class of Fractional Kirchhoff Equation Involving Exponential Nonlinearity.

This article deals with the following fractional N s -Laplace Kichhoff equation involving exponential growth of the form: ε N K [ u ] s , N s N s (- Δ) N / s s u + Z (x) | u | N s - 2 u = f (u) in R N , <graphic href="12220_2024_1707_Article_Equ120.gif"></graphic> where ε > 0 is a parameter, s ∈ (0 , 1) and (- Δ) p s is the fractional p-Laplace operator with p = N s ≥ 2 , K is a Kirchhoff function, f is a continuous function with exponential growth and Z is a potential function possessing a local minimum. Under some suitable conditions, we obtain the existence, multiplicity and concentration of solutions to the above problem via penalization methods and Lyusternik-Schnirelmann theory. [ABSTRACT FROM AUTHOR]