Auxiliary kernels method and stability of solutions of weakly nonlinear volterra integro - differential equation of the fourth order with incomplete kernels
Sufficient conditions are established for the boundedness on the semi - axis of all solutions and their first, second and third derivatives i.e., for the stability of solutions to a weakly non - linear fourth - order integro - differential equation of the Volterra type. For this purpose the method of auxiliary kernels, the non - standard method of reduction to a system, the method of transformation of V. Volterra equations, the method of cutting functions and the method of integral inequalities are used and developed. An illustrative example is constructed.