Essential spectrum of systems of singular differential equations

F. V. Atkinson, H. Langer, R. Mennicken and A. A. Shkalikov, The essential spectrum of some matrix operators, Math. Nachr., 167 (1994), 5–20.

H. R. Beyer, The spectrum of adiabatic stellar oscillations, J. Math. Phys., 36 (1995), 4792–4814.

J. W. Calkin, Symmetric transformations in Hilbert space, Duke Math. J., 7 (1940), 504–508.

S. Chandrasekhar, An introduction to the study of stellar structure, Dover Publications Inc., New York, N. Y., 1957.

J. Descloux and G. Geymonat, On the essential spectrum of an operator relative to the stability of a plasma in toroidal geometry, École polytechnique Fédérale de Lausanne, Lausanne, 1979, preprint.

J. Descloux and G. Geymonat, Sur le spectre essentiel d’un opérateur relatif à la stabilité d’un plasma en géométrie toroïdale, C. R. Acad. Sci. Paris Sér. A-B, 290 (1980), A795–A797.

D. E. Edmunds and W. D. Evans, Spectral theory and differential operators, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1987.

M. Faierman, R. Mennicken and M. Möller, The essential spectrum of a model problem in 2-dimensional magnetohydrodynamics: a proof of a conjecture by J. Descloux and G. Geymonat, Math. Nachr., 269/270 (2004), 129–149.

M. Faierman and M. Möller, On the essential spectrum of a differentially rotating star in the axisymmetric case, Proc. Roy. Soc. Edinburgh Sect. A, 130 (2000), 1–23.

I. M. Glazman, Direct methods of qualitative spectral analysis of singular differential operators, Translated from the Russian by the IPST staff, Israel Program for Scientific Translations, Jerusalem, 1966.

G. Grubb and G. Geymonat, The essential spectrum of elliptic systems of mixed order, Math. Ann., 227 (1977), 247–276.

T. Kako, Essential spectrum of linearized operator for MHD plasma in cylindrical region, Z. Angew. Math. Phys., 38 (1987), 433–449.

A. Yu. Konstantinov, Spectral theory of some matrix differential operators of mixed order, Ukrain. Mat. Zh., 50 (1998), 1064–1072.

A. Yu. Konstantinov and R. Mennicken, On the Friedrichs extension of some block operator matrices, Integral Equations Operator Theory, 42 (2002), 472–481.

P. Kurasov, I. Lelyavin and S. Naboko, On the essential spectrum of a class of singular matrix differential operators. II. Weyl’s limit circles for the Hain-Lüst operator whenever quasi-regularity conditions are not satisfied, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 109–138.

P. Kurasov and S. Naboko, Essential spectrum due to singularity, J. Nonlinear Math. Phys., 10 (2003), 93–106.

T. Kusche, R. Mennicken and M. Möller, Friedrichs extension and essential spectrum of systems of differential operators of mixed order, Math. Nachr., 278 (2005), 1591–1606.

H. Langer and M. Möller, The essential spectrum of a non-elliptic boundary value problem, Math. Nachr., 178 (1996), 233–248.

M. Marletta and C. Tretter, Essential spectra of coupled systems of differential equations and applications in hydrodynamics, J. Differential Equations, 243 (2007), 36–69.

R. Mennicken, S. Naboko and C. Tretter, Essential spectrum of a system of singular differential operators and the asymptotic Hain-Lüst operator, Proc. Amer. Math. Soc., 130 (2002), 1699–1710 (electronic).

J. Qi and Sh. Chen, Essential spectra of singular matrix differential operators of mixed order, J. Differential Equations, 250 (2011), 4219.4235.

J. Qi and Sh. Chen, Essential spectra of singular matrix differential operators of mixed order in the limit circle case, Math. Nachr., 284 (2011), 342–354.

G. D. Raǐkov, The spectrum of a linear magnetohydrodynamic model with cylindrical symmetry, Arch. Rational Mech. Anal., 116 (1991), 161–198.

F. Riesz and B. Sz.-Nagy, Functional analysis, Dover Publications Inc., New York, 1990.

C. Tretter, Spectral theory of block operator matrices and applications, Imperial College Press, London, 2008.