# Riesz basis property of the system of eigenfunctions for a non-linear problem of Sturm-Liouville type

## Abstract

For a non-linear eigenvalue problem similar to a linear Sturm-Liouville problem the properties of the spectrum and the eigenfunctions are analysed. The system of eigenfunctions is shown to be a Riesz basis in L{sub 2}.

- Authors:

- Joint Institute for Nuclear Research, Dubna, Moscow region (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21202928

- Resource Type:
- Journal Article

- Journal Name:
- Sbornik. Mathematics

- Additional Journal Information:
- Journal Volume: 191; Journal Issue: 3; Other Information: DOI: 10.1070/SM2000v191n03ABEH000461; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENFUNCTIONS; EIGENVALUES; NONLINEAR PROBLEMS; SPECTRA; STURM-LIOUVILLE EQUATION

### Citation Formats

```
Zhidkov, P E.
```*Riesz basis property of the system of eigenfunctions for a non-linear problem of Sturm-Liouville type*. United States: N. p., 2000.
Web. doi:10.1070/SM2000V191N03ABEH000461; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Zhidkov, P E.
```*Riesz basis property of the system of eigenfunctions for a non-linear problem of Sturm-Liouville type*. United States. doi:10.1070/SM2000V191N03ABEH000461; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Zhidkov, P E. Sun .
"Riesz basis property of the system of eigenfunctions for a non-linear problem of Sturm-Liouville type". United States. doi:10.1070/SM2000V191N03ABEH000461; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
```

```
@article{osti_21202928,
```

title = {Riesz basis property of the system of eigenfunctions for a non-linear problem of Sturm-Liouville type},

author = {Zhidkov, P E},

abstractNote = {For a non-linear eigenvalue problem similar to a linear Sturm-Liouville problem the properties of the spectrum and the eigenfunctions are analysed. The system of eigenfunctions is shown to be a Riesz basis in L{sub 2}.},

doi = {10.1070/SM2000V191N03ABEH000461; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},

journal = {Sbornik. Mathematics},

issn = {1064-5616},

number = 3,

volume = 191,

place = {United States},

year = {2000},

month = {4}

}

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