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This paper is intended to discuss the problems of solving system of linear operator equations and a kind of nonlinear operator equation A u B u + C u = f . For system of linear operator equations, we obtain a criterion about the existence of solutions. If it has solutions, we get the analytic representation of its minimum norm solution and the structure of its solution space; for nonlinear operator equation A u B u + C u = f , with the help of the discussion on how to solve the system of linear operator equations, the exact solution is given. Besides, we obtain the representation of all its solutions.

In this paper, we will introduce the concept of affine frame in wavelet analysis to the field of p-adic number, hence provide new mathematic tools for application of p-adic analysis.

In this work, we give a new method for solving a nonlinear partial differential equation in the reproducing kernel space. Through numerical example, it is proved to be valid.