Lukash K. Properties of solutions of two-parameter discrete Volterra system

The necessary and sufficient conditions for the existence of the unique bounded or summable with p-th power solution for the linear two-parameter Volterra system with operator coefficients are obtained. The sufficient conditions for boundedness of the nonlinear two-parameter discrete Volterra system's solution are obtained. This result is based on the general theorem about the contracting mapping for the Volterra equation, that has been proved in the thesis. The necessary and sufficient conditions for boundedness in p-th order mean of the stochastic linear two-parameter Volterra system's solution and sufficient conditions for boundedness in p-th order mean of the stochastic nonlinear two-parameter Volterra system's solution are obtained. The solution stability for the small coefficient disturbances are proved.