Solution of one Volterra type nonlinear integral equation on positive semi-axis

The work is devoted to the investigation of one class of Volterra type nonlinear integral equations on positive half-line. The specified class of equations except for self-interest in mathematics has also important applications in physical kinetics. The combination of special factorization methods with methods of construction of invariant cone segments allows us to construct a non-negative solution of initial equation, and investigate integral asymptotics of that solution at infinity.