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Generalization of an integro-transcendetnal equation system with vanishing solutions in free phase problem

The nonlinear integral equation of Hammerstein type with the linear dependence of the argument of unknown function and nonlinear dependency on its modulus is considered. Solutions of this equation are represented by means of polynomials of finite degree describing, in particular, zeros of these solutions. For the case of solutions vanishing in the considered interval, new system of integro-transcendental equation is obtained.