## Rocky Mountain Journal of Mathematics

- Rocky Mountain J. Math.
- Volume 48, Number 6 (2018), 1763-1779.

### Eigenvalue problem associated with the fourth order differential-operator equation

Nigar M. Aslanova, Mamed Bayramoglu, and Khalig M. Aslanov

#### Abstract

In this paper, we investigate the boundary value problem for fourth order differential operator equations with unbounded operator coefficients and one $\lambda $-dependent boundary condition. We obtain an asymptotic formula for eigenvalues and a trace formula for the corresponding self-adjoint operator.

#### Article information

**Source**

Rocky Mountain J. Math., Volume 48, Number 6 (2018), 1763-1779.

**Dates**

First available in Project Euclid: 24 November 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.rmjm/1543028436

**Digital Object Identifier**

doi:10.1216/RMJ-2018-48-6-1763

**Zentralblatt MATH identifier**

06987223

**Subjects**

Primary: 34B05: Linear boundary value problems 34G20: Nonlinear equations [See also 47Hxx, 47Jxx] 34L05: General spectral theory 34L20: Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A10: Spectrum, resolvent

**Keywords**

Hilbert space differential operator equation spectrum eigenvalues trace class operators regularized trace

#### Citation

Aslanova, Nigar M.; Bayramoglu, Mamed; Aslanov, Khalig M. Eigenvalue problem associated with the fourth order differential-operator equation. Rocky Mountain J. Math. 48 (2018), no. 6, 1763--1779. doi:10.1216/RMJ-2018-48-6-1763. https://projecteuclid.org/euclid.rmjm/1543028436