Variational characterizations of real eigenvalues of selfadjoint operators on a Hilbert space depending nonlinearly on an eigenparameter usually assume differentiable dependence of the operator on the eigenparameter. In this paper we generalize these results to nonlinear problems which depend only continuously on the parameter. This result is applied to a class of variational eigenvalue problem...

The research is financed by the Natural Science Foundation of China and the National Natural Science Foundation of Neimongo. No. 10661008 and 200711020102 (Sponsoring information) Abstract In this paper, we consider an indefinite Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions. In an appropriate space K, we define a new self-adjoint operato...

In this work, we investigate a Dirac system which has discontinuities at finite interior points and contains eigenparameter in both boundary transmission conditions. By defining suitable Hilbert space H associated with the problem, generate self-adjoint operator T such that eigenvalues of considered problem coincide those T. We construct fundamental solutions get asymptotic formulas for solutio...

In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining  a new Hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

in this manuscript, we study the inverse problem for non self-adjoint sturm--liouville operator $-d^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. by defining  a new hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...