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# Eigenfunction expansions associated with an operator differential equation non-linearly depending on a spectral parameter

### Abstract

For an operator differential equation that depends on a spectral parameter in the Nevanlinna manner we obtain expansions in eigenfunctions.

Key words: Relation generated by pair of differential expressions one of which depends on spectral parameter in nonlinear manner, non-injective resolvent, generalized resolvent, Weyl type operator function and solution, eigenfunction expansion.

### Article Information

 Title Eigenfunction expansions associated with an operator differential equation non-linearly depending on a spectral parameter Source Methods Funct. Anal. Topology, Vol. 20 (2014), no. 1, 68-91 MathSciNet MR3242124 zbMATH 1313.34276 Milestones Received 09/07/2013; Revised 07/09/2013 Copyright The Author(s) 2014 (CC BY-SA)

### Authors Information

Volodymyr Khrabustovskyi
Ukrainian State Academy of Railway Transport, Kharkiv, Ukraine

### Citation Example

Volodymyr Khrabustovskyi, Eigenfunction expansions associated with an operator differential equation non-linearly depending on a spectral parameter, Methods Funct. Anal. Topology 20 (2014), no. 1, 68-91.

### BibTex

@article {MFAT702,
AUTHOR = {Khrabustovskyi, Volodymyr},
TITLE = {Eigenfunction expansions associated with an operator differential equation non-linearly depending on a spectral parameter},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {20},
YEAR = {2014},
NUMBER = {1},
PAGES = {68-91},
ISSN = {1029-3531},
MRNUMBER = {MR3242124},
ZBLNUMBER = {1313.34276},
URL = {http://mfat.imath.kiev.ua/article/?id=702},
}