One approximate solution of the Nekrasov problem

An approximate solution $\omega=A[\omega,\mu]$ of the nonlinear integral Nekrasov equation is obtained by successive replacement of the kernel of the integral operator by a close one. The solution is sought not directly at the bifurcation point $\mu_1=3$ of the linearized equation $\omega=\mu L[\omega]$ but at the point $\mu=1$ at which operator $A[\omega,\mu]$, remaining nonlinear in $\omega$, is linear in $\mu$.