In a real Hilbert space we consider the following singularly perturbed Cauchy problem
are two small parameters, is a linear self-adjoint operator and is a nonlinear Lipschitzian operator.
We study the behavior of solutions in two different cases:
and relative to solution to the corresponding unperturbed problem.
We obtain some a priori estimates of solutions to the perturbed problem, which are uniform with respect to parameters, and a relationship between solutions to both problems. We establish that the solution to the unperturbed problem has a singular behavior, relative to the parameters, in the neighbourhood of