A Linearization for a Class of -Nonlinear Boundary Eigenvalue Problems

In this paper a new linearization of boundary eigenvalue problems for systems Qy0 C e A0 Qy D e A1 Qy of n rst order differential equations with -polynomial boundary conditions is proposed. The linearized problem is again a boundary eigenvalue problem for a system y0 CA0y D A1y of rst order differential equations of dimension nCnO where nO is the total polynomial degree of the boundary conditions. As a particular case, we consider systems of rst order differential equations induced by nth order differential equations N D P , and we give an application to the Orr–Sommerfeld equation with -quadratic boundary conditions.