System of three identical spinless bosons interacting by means of two-particle potentials of the finite range is considered. The Schrödinger equation is reduced to the problem with boundary conditions, with the aid of the assumption that the logarithmic derivative of the wave function on the potential surface does not depend on the third particle position outside the six-dimensional sphere with the radius $R$ in configuration space. In this region the ratio $r_0/R$ is a small parameter. In the lowest approximation with respect to this parameter the sequence of the boundary problem solutions at zero total energy is found. It is shown that for constructing the wave function, the generalized Fourier method can be applied, the elementary solutions of which coincide with the functions obtained.