Eigenfunction expansions associated with an operator differential equation nonlinearly depending on a spectral parameter. (English) Zbl 1313.34276

Khrabustovskyi, Volodymyr

Methods Funct. Anal. Topol. 20, No. 1, 68-91 (2014).

The author obtains eigenfunction expansions for operator-differential equations of the form \[ l[y]-\lambda m[y]-n_\lambda [y]=m[f], \] where \(l,m,n_\lambda\) are symmetric differential expressions with bounded operator coefficients on a Hilbert space, \(n_\lambda\) is a Nevanlinna function of the spectral parameter \(\lambda\). The case \(n_\lambda =0\) was considered in the same generality in the author’s earlier paper [Methods Funct. Anal. Topol. 15, No. 2, 137–151 (2009; Zbl 1199.34450)].

Reviewer: Anatoly N. Kochubei (Kyïv)

MSC:

34L10	Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
34B07	Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter
34G10	Linear differential equations in abstract spaces
47E05	General theory of ordinary differential operators

Keywords:

operator-differential equation; Nevanlinna function; eigenfunction expansions

Citations:

Zbl 1199.34450