On a nonlinear eigenvalue problem

In the present paper we consider a selfadjoint and nonsmooth operator-valued function on (c, d)R¹. We suppose that the equation (L()x, x)=0,x0, has exactly one rootp(x) (c, d) and the functionf()=(L()x, x) is increasing at the pointp(x). We discuss questions of the variational theory of the spectrum. Some theorems on the variational properties of the spectrum are proved.