A linearization for a class of λ-nonlinear boundary eigenvalue problems

In this paper a new linearization of boundary eigenvalue problems for systems (y) over tilde' + (A) over tilde(0)(y) over tilde = lambda (A) over tilde(1)(y) over tilde of n first order differential equations with lambda-polynomial boundary conditions is proposed. The linearized problem is again a boundary eigenvalue problem for a system y' + A(0)y = lambda A(1)y of first order differential equations of dimension n + (n) over cap where (n) over cap is the total polynomial degree of the boundary conditions. As a particular case, we consider systems of first order differential equations induced by nth order differential equations N eta = lambda P eta, and we give an application to the Orr-Sommerfeld equation with lambda-quadratic boundary conditions. (C) 2000 Academic Press.