Regularized Seidel-Newton method and nonlinear problems at resonance (Q1915886)

This paper continues a series of earlier articles on the Seidel-Newton method by the first author and various collaborators [see e.g. the first author and \textit{Bui Doc Tien}, J. Math. Viet., 22, No. 3-4, 83-109 (1994)]. A regularized form of the Seidel-Newton method is introduced for solving a nonlinear operator equation \(Ax+ F(x)= 0\) involving a bounded linear Fredholm operator \(A\) and a \(C^1\)-mapping \(F\) between real Banach spaces. The local convergence of the method is proved and, as an example, a periodic boundary value problem for the nonlinear Duffing-Van-der-Pol equation is discussed.