Multiplicity and concentration of normalized solutions for a Kirchhoff type problem with L2-subcritical nonlinearities

In this paper, we studied the existence of multiple normalized solutions to the following Kirchhoff type equation: {-(a epsilon(2)+b epsilon integral(R3)|del u|(2)dx)Delta u+V(x)u=mu u+f(u) in R-3, integral(R3)|u|(2)dx=m epsilon(3),u is an element of H-1(R-3), where a, b, m>0, epsilon is a small positive parameter, V is a nonnegative continuous function, f is a continuous function with L-2-subcritical growth and mu is an element of R will arise as a Lagrange multiplier. Under the suitable assumptions on V and f, the existence of multiple normalized solutions was obtained by using minimization techniques and the Lusternik-Schnirelmann theory. We pointed out that the number of normalized solutions was related to the topological richness of the set where the potential V attained its minimum value.