EXISTENCE AND QUASILINEARIZATION FOR A CLASS OF NONLINEAR ELLIPTIC SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS

In this paper we discuss some existence results and the application of quasilinearization methods to the solution of second order nonlinear self adjoint elliptic partial differential equation in Rⁿ with Dirichlet boundary conditions. Under fairly general assumptions on the data of the problem we show the existence of a solution that can be obtained as the limit of a quadratically convergent nondecreasing sequence of approximate solutions. If the assumptions are strengthened, we show that the solution can be quadratically bracketed between two monotone sequences of approximate solutions of certain related linear equations.