We consider both the Cauchy problem and the boundary value problem studied by Cesari [L. Cesari, Riv. Mat. Univ. Parma (3) 3 (1974), 107-131] for canonic system in diagonal form. We give a theoretical estimate of the effect of the nonlinear perturbation on the solution, that is, we establish a theoretical estimate of the difference between the solution of the nonlinear problem and the solution of the linear one.
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