This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...

In this paper we survey variational characterizations of eigenvalues of nonlinear eigenproblems, i.e. generalizations of Rayleigh’s principle, the minmax characterization of Poincaré, and the maxmin characterization of Courant, Fischer and Weyl to eigenvalue problems containing the eigenparameter nonlinearly. In this note we consider the nonlinear eigenvalue problem