How to solve nonlinear operator equation A(v2)+Cv=f

摘要

In this paper, we discuss the problems of how to solve linear operator equation in Hilbert spaces and a kind of nonlinear operator equation A(v2)+Cv=f in reproducing kernel space W21[a,b]. For linear operator equation, 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(v2)+Cv=f, by using the method of solving linear operator equation, one exact solution is given. Besides, we obtain the representation of its solution set. Final examples show our methods are effective.