The authors consider the following equation of first kind \(Ax=y\in Y\) with respect to \(x\in X\) where A is a monotone potential operator from a reflexive Banach space X into its dual Y. In order to regularize this equation as an addition to their previous works the authors suggest to solve the equation \(Ax+\alpha Ux=y_{\delta}\) by minimizing the functional \(\omega (x)-<y_{\delta},\quad x>+\alpha \| x\|^ 2/2\) where \(\omega\) is a potential of A, \(\alpha\) is the chosen regularization parameter, U is the duality operator from X onto Y and \(y_{\delta}\) is an approximation of y. As an example the Dirichlet problem for a quasi- linear elliptic degenerated equation is considered.