Suppose we have system of differential equations:
$$f_i'(x)=A_i(f_1,\cdots,f_n,x),$$
where $A_i$ is nonlinear functional of $f_i$ and $x$.
As initial conditions I have $f_i(x_0)=g_i(x_0,B)$, where $B$ depends on solution: $B=\int^{\infty}_0f_1^2(y)ydy$ (one could take different explicit form).
Is there name for such type of initial value problem? Could you give me any sources where I can read about it?