Advances in Differential Equations

Elliptic differential-operator problems with a spectral parameter in both the equation and boundary-operator conditions

B. A. Aliev and Ya. Yakubov

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Abstract

We consider boundary value problems for elliptic differential-operator equations with the spectral parameter and operator-boundary conditions containing a parameter of the same order as the equation. An isomorphism and the corresponding estimate of a solution (with respect to the space variable and the parameter) are obtained. Then, discreteness of the spectrum and completeness of a system of root functions of the corresponding homogeneous problem are established. Finally, an application is given of the abstract results obtained on the isomorphism and the completeness to boundary value problems for elliptic differential equations with a parameter in non-smooth domains.

Article information

Source
Adv. Differential Equations Volume 11, Number 10 (2006), 1081-1110.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867601

Mathematical Reviews number (MathSciNet)
MR2279710

Zentralblatt MATH identifier
1162.34046

Subjects
Primary: 34G10: Linear equations [See also 47D06, 47D09]
Secondary: 34L10: Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions 35J25: Boundary value problems for second-order elliptic equations 35P10: Completeness of eigenfunctions, eigenfunction expansions 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47) 47N20: Applications to differential and integral equations

Citation

Aliev, B. A.; Yakubov, Ya. Elliptic differential-operator problems with a spectral parameter in both the equation and boundary-operator conditions. Adv. Differential Equations 11 (2006), no. 10, 1081--1110. https://projecteuclid.org/euclid.ade/1355867601.


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