Abstract
We establish generalized orthogonality conditions and prove a theorem on completeness of the collection of eigenfunctions of a spectral problem with boundary and conjugating conditions depending on a parameter for piecewise homogeneous bounded connected and disconnected domains.
Similar content being viewed by others
References
A. N. Komarenko, I. A. Lukovskii, and S. F. Feshchenko, “To the problem of eigenvalues with boundary conditions depending on a parameter,”Ukr. Mat. Zh.,17, No. 6, 740–748 (1965).
G. N. Komarov, “On eigenfunctions and eigenvalues of systems of differential equations and decomposition of an arbitrary vector function,”Mat. Fiz., Issue 4, 66–77 (1968).
A. A. Berezovskii and L. P. Nizhnik, “Electromagnetic field in a rectangular waveguide with conducting walls,” in:Boundary-Value Problems in Mathematical Physics [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1971), pp. 52–59.
Yu. A. Mitropol'skii, L. P. Nizhnik, and V. L. Kul'chitskii,Nonlinear Problems of Heat Conduction with Time Derivative in Boundary Conditions [in Russian], Preprint No. 74.15, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1974).
L. M. Berezovskaya, “Nonstationary thermal fields of heat conducting walls with strongly varying thermal characteristics,” in:Boundary-Value Problems in Mathematical Physics [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1978), pp. 12–21.
L. P. Nizhnik and L. A. Taraborkin, “Boundary-value problems for the heat conduction equation with time derivative in conjugating conditions,”Ukr. Mat. Zh.,34, No. 1, 121–126 (1982).
G. N. Komarov and I. A. Motovilovets, “Nonstationary thermal field of a laminated wall,” in:Partial Differential Equations in Applied Problems [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1986), pp. 52–60.
G. N. Komarov, “Conjugating conditions across a thermally thin layer in problems of heat conduction,” in:Boundary-Value Problems in Mathematical Physics [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1994), pp. 56–62.
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1653–1660, December, 1995.
Rights and permissions
About this article
Cite this article
Komarov, G.N. Spectral problems with boundary and conjugating conditions depending on a parameter. Ukr Math J 47, 1889–1897 (1995). https://doi.org/10.1007/BF01060962
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01060962