Eigenfunction expansions associated with an operator differential equation nonlinearly depending on a spectral parameter
The author obtains eigenfunction expansions for operator-differential equations of the form NEWLINE\[NEWLINEl[y]-\lambda m[y]-n_\lambda [y]=m[f],NEWLINE\]NEWLINE 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)].
scientific article; zbMATH DE number 6333573