Zeros of solutions of functional equations in the space of discontinuous functions of two variables (Q2484183)

The distribution of zeros of solutions of functional equations in the space of functions of two variables is studied. A zero of a solution in the space of noncontinuous functions is defined. It is demonstrated that oscillatory properties of functional equations are determined by the spectral radius of a corresponding operator acting in the space of essentially bounded functions. Zones of positivity of solutions are estimated. Various exact oscillation and non-oscillation tests are proposed. A necessary and sufficient conditions of oscillation is obtained.