On the existence of a resolvent and separability for a class of singular hyperbolic type differential operators on an unbounded domain
Eurasian mathematical journal, Tome 7 (2016) no. 1, pp. 50-67.

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In the present work the existence of a resolvent and separability for a class of hyperbolic type operators with increasing coefficients in an unbounded domain are proved.
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M. Muratbekov; M. Otelbaev. On the existence of a resolvent and separability for a class of singular hyperbolic type differential operators on an unbounded domain. Eurasian mathematical journal, Tome 7 (2016) no. 1, pp. 50-67. http://geodesic.mathdoc.fr/item/EMJ_2016_7_1_a3/

[1] K.Kh. Boimatov, “The separability theorems, weights spaces and their applications”, Proc. of Math. Inst. AN USSR, 170, 1984, 37–76 (in Russian) | MR

[2] K.Kh. Boimatov, “The separability theorems, weights spaces and their applications”, Proc. of Math. Inst. AN USSR, 38:4 (1989), 157–160 | MR

[3] K. Ospanov, “Qualitative and approximate characteristics of solutions of Beltrami type systems”, Complex Variables and Elliptic Equations, 60:7 (2015), 1005–1014 | DOI | MR | Zbl

[4] K. Ospanov, R.D. Akhmetkaliyeva, “Separation and the existence theorem for second order nonlinear differential equation”, Electronic Journal of Qualitative Theory of Differential Equations, 66 (2012), 1–12 | DOI | MR

[5] M.B. Muratbekov, M.M. Muratbekov, K.N. Ospanov, “On approximate properties of solutions of a nonliner mixed-type equation”, Journal of Mathematical Sciences, 150:6 (2008), 2521–2530 | DOI | MR | Zbl

[6] M.B. Muratbekov, M.M. Muratbekov, “Estimates of the spectrum for a class of mixed type operators”, Diff. equations, 42:1 (2007), 1–4 | MR

[7] M.B. Muratbekov, M.M. Muratbekov, K.N. Ospanov, “Coercive solvability of odd-order differential equations and its applications”, Dokl. Mathematics, 82:3 (2010), 1–3 | DOI | MR

[8] M.B. Muratbekov, M.M. Muratbekov, A.M. Abylayeva, “On existence of the resolvent and discreteness of the spectrum of a class of differential operators of hyperbolic type”, Electronic Journal of Qualitative Theory of Differential Equations, 64 (2013), 1–10 | DOI | MR

[9] M.B. Muratbekov, “Separability of an operator of mixed type and the completeness of its root vectors”, Diff. Equations, 27 (1991), 1517–1526 | MR | Zbl

[10] M. Muratbekov, K. Ospanov, S. Igisinov, “Solvability of a class of mixed type second order equations and nonlocal estimates”, Applied Mathematics Letters, 25 (2012), 1661–1665 | DOI | MR | Zbl

[11] M.B. Muratbekov, “Two-sides estimates of the distribution function of s-values of a class of mixed type differential operators”, Complex Variables and Elliptic Equations, 52 (2007), 1121–1144 | DOI | MR | Zbl

[12] M. Guzman, Differentiation of integrals in $R^n$, Springer-Verlag, Berlin–Heidelberg–New York, 1975 | MR

[13] M. Nagumo, Lectures on modern theory of partial differential equations, Mir, M., 1967 (in Russian) | MR

[14] M. Otelbaev, “On separability of elliptic operators”, Doklady AN USSR, 234:3 (1977), 540–543 (in Russian) | MR | Zbl

[15] M. Otelbaev, “Coercive estimates and separability theorems for elliptic equations in $R^n$”, Trudy Mat. Inst. Steklov, 161, 1983, 195–217 (in Russian) | MR | Zbl

[16] T. Kato, Perturbation theory for linear operators, Springer-Verlag, Berlin–Heidelberg–New York, 1966 | MR | Zbl

[17] W.N. Everitt, M. Giertz, “Some properties of the domains of certain differential operators”, Proc. London Math. Soc., 23:2 (1971), 301–324 | DOI | MR | Zbl

[18] W.N. Everitt, M. Giertz, “On properties of the powers of a formally self-adjoint differential expression”, Proc. London Math. Soc., 24:1 (1972), 149–170 | DOI | MR | Zbl

[19] W.N. Everitt, M. Giertz, “On some properties of the domains of power of certain differential operators”, Proc. London Math. Soc., 24:4 (1972), 756–768 | DOI | MR | Zbl

[20] W.N. Everitt, M. Giertz, “An example conserning the separation property for differential operators”, Proc. Roy. Soc., Edinburgh, 71 (1972), 159–165 | MR