Analogs of generalized resolvents of relations generated by pair of differential operator expressions one of which depends on spectral parameter in nonlinear manner

TL;DR

This paper constructs analogs of generalized resolvents for relations generated by pairs of differential operator expressions, where one depends nonlinearly on the spectral parameter, expanding the theoretical framework for such operators.

Contribution

It introduces a method to construct integro-differential analogs of generalized resolvents for differential relations with nonlinear spectral dependence.

Findings

Constructed analogs of generalized resolvents as integro-differential operators.

Extended the theory to relations with spectral parameter dependence in the Nevanlinna manner.

Provided a new approach for analyzing differential relations with nonlinear spectral dependence.

Abstract

For the relations generated by pair of differential operator expressions one of which depends on the spectral parameter in the Nevanlinna manner we construct analogs of the generalized resolvents which are integro-differential operators.