Existence of solutions for a class of fractional Kirchhoff variational inequality

We are concerned with the following fractional Kirchhoff variational inequality: (a + b[u] (2) ) integral(3)(R) ( - Delta) (s/2) u( - Delta)( s /2 )(v - u) dx + integral(R) 3 (1 + lambda V (x))u(v - u) dx >= integral(R)3 f (u)(v - u) dx V v E K , where s is an element of (( 3)/ (4) , 1) , lambda > 0 . In this paper, by applying penalization techniques from Bensoussan and Lions (1978) combined with mountain pass theorem, we show the existence and concentration behavior of positive solution to the cited variational inequality. This result extend some results established by Alves, Barros and Torres [J. Math. Anal. Appl. 494 (2021)] to the fractional case.