Nonradial normalized solutions for nonlinear scalar field equations

We study the following nonlinear scalar field equation {-Delta u -f(u) - mu u in R-N, parallel to u parallel to(2)(L2(RN)) = m, u is an element of H-1(R-N). Here f is an element of C(R, R), m > 0 is a given constant and mu is an element of R arises as a Lagrange multiplier. In a mass subcritical case but under general assumptions on the nonlinearity f, we show the existence of one nonradial solution for any N >= 4, and obtain multiple (sometimes infinitely many) nonradial solutions when N = 4 or N >= 6. In particular, all these solutions are sign-changing.