### Abstract

We study an eigenvalue problem in the framework of difference equations. We show that there exist two positive constants λ_{0} and λ_{1} verifying λ_{0} ≤ λ_{1} such that any λ ∈ (0, λ_{0}) is not an eigenvalue of the problem, while any λ ∈ [λ_{1}, ∞) is an eigenvalue of the problem. Some estimates for λ_{0} and λ_{1} are also given.

Original language | English |
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Pages (from-to) | 1015-1029 |

Number of pages | 15 |

Journal | Communications in Contemporary Mathematics |

Volume | 12 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 2010 |

### Fingerprint

### Keywords

- continuous spectrum
- critical point
- discrete boundary value problem
- Eigenvalue problem

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications in Contemporary Mathematics*,

*12*(6), 1015-1029. https://doi.org/10.1142/S0219199710004093

**Spectral estimates for a nonhomogeneous difference problem.** / Kristály, A.; Mihǎilescu, Mihai; Rǎdulescu, Vicenţiu; Tersian, Stepan.

Research output: Contribution to journal › Article

*Communications in Contemporary Mathematics*, vol. 12, no. 6, pp. 1015-1029. https://doi.org/10.1142/S0219199710004093

}

TY - JOUR

T1 - Spectral estimates for a nonhomogeneous difference problem

AU - Kristály, A.

AU - Mihǎilescu, Mihai

AU - Rǎdulescu, Vicenţiu

AU - Tersian, Stepan

PY - 2010/12

Y1 - 2010/12

N2 - We study an eigenvalue problem in the framework of difference equations. We show that there exist two positive constants λ0 and λ1 verifying λ0 ≤ λ1 such that any λ ∈ (0, λ0) is not an eigenvalue of the problem, while any λ ∈ [λ1, ∞) is an eigenvalue of the problem. Some estimates for λ0 and λ1 are also given.

AB - We study an eigenvalue problem in the framework of difference equations. We show that there exist two positive constants λ0 and λ1 verifying λ0 ≤ λ1 such that any λ ∈ (0, λ0) is not an eigenvalue of the problem, while any λ ∈ [λ1, ∞) is an eigenvalue of the problem. Some estimates for λ0 and λ1 are also given.

KW - continuous spectrum

KW - critical point

KW - discrete boundary value problem

KW - Eigenvalue problem

UR - http://www.scopus.com/inward/record.url?scp=78650720294&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650720294&partnerID=8YFLogxK

U2 - 10.1142/S0219199710004093

DO - 10.1142/S0219199710004093

M3 - Article

AN - SCOPUS:78650720294

VL - 12

SP - 1015

EP - 1029

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

SN - 0219-1997

IS - 6

ER -