Rapid convergence for nonlinear fourth-order quasilinear elliptic equations

Abstract

Combining with variational method and lower and upper solutions, we get a quasilinearization method which construct an iterative scheme converging to a solution of a nonlinear fourth-order problem involving the p -Laplacian. At the same time, the result of K -th order convergence for the nonlinear fourth-order problem is obtained via the idea of Taylors approximation.