ON MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR FRACTIONAL p-LAPLACE CHOQUARD-KIRCHHOFF EQUATIONS

In this paper, we consider the Choquard-Kirchhoff involving fractional p-Laplace equation of the form: M(epsilon(sp-N)[u](p)(s,p)+epsilon(-N)integral(N)(R) V(x)|u|(p)dx) (epsilon(sp)(-triangle)(s)p u+V(x)|u|(p-2)u)) =epsilon(mu-N)(1/|x|(mu)*F(u))f(u) in R-N, where epsilon > 0 is a parameter, s is an element of (0, , 1), 0 < mu < ps, (-triangle)(p)(s) is the fractional p-Laplacian operator, M represents Kirchhoff function, V is a continuous potential function and f is a continuous function involving sub critical growth. With the help of well-known penalization methods and Ljusternik-Schnirelmann theory, we obtain the existence, multiplicity and concentration of solutions for the above equations.