Mutual transformation of vanishing and nonvanishing solutions of a class of nonlinear Hammerstein integral equations

A class of nonlinear integral equations of the Hammerstein type connected with the phase optimization problem (antenna synthesis, energy transmitting lines optimization etc.), which have analytical solutions, is considered. The paper develops the early obtained results about connection between the sets of solutions, with or without zeros in their definition domains. The process of mutual transformation of different types of results is numerically analyzed, and other types of branching are investigated.