Multiplicity of nontrivial solutions for a class of fractional Kirchhoff equations

In this article, we study a class of fractional Kirchhoff with a superlinear nonlinearity: {( RN |(-o)alpha 2 u|2dx)(-o)alpha u + A.V(x)u = f(x, u) in RN, u is an element of H alpha(RN), N >= 1, (1.1) where lambda > 0 is a parameter, a and b are positive numbers satisfying M(t) = am(t) + b, m : R+ -> R+ is continuous. V : RN x R -> R is continuous. f satisfies lim f(x, t)/|t|k-1 = Q(x) uniformly in x is an element of RN |t|->infinity for each 2 < k < 2*alpha, (2*alpha = 2N N-2 alpha). We investigated the effects of functions m and Q on the solution. By applying the variational method, we obtain the existence of multiple solutions. Furthermore, it is worth mentioning that the ground state solution has also been obtained.