Generalized quasilinearization for quasilinear parabolic equations with nonlinearities of DC type

In this paper, we consider an initial boundary-value problem for a class of quasilinear parabolic equations whose lower-order nonlinearity is of d.c. function type with respecxt to the dependent variable. Assuming the existen ce of an ordered pair of weak upper and lower solutions, we establish a gen eralized quasilinearization method for the problem under consideration. A c haracteristic feature of this generalized quasilinearization method consist s in the construction of monotone sequences converging to the unique soluti on within the interval of upper and lower solutions, and whose convergence rate is quadratic.