Ritz method for equations with small parameters for higher derivatives

The problem of convergence of the Ritz method is considered for positive definite operational equations of the form $a_\varepsilon u\equiv(\varepsilon A_1+A_0)u=f$ containing small parameters $\varepsilon$ for the principal part. For specific natural conditions it is proved that the Ritz method, used for an approximate solution to such equations, converges to an exact solution in a metric with quadratic form uniformly with respect to the parameter $\varepsilon$.