Taiwanese Journal of Mathematics

On Normal Solvability of Boundary Value Problems for Operator-differential Equations on Semi-axis in Weight Space

Sabir S. Mirzoev and Rovshan Z. Humbataliev

Full-text: Open access

Abstract

In the paper, the conditions of normal solvability of some boundary value problems are obtained for a class of operator-differential equations of elliptic type on a semi-axis in weight spaces. The principal part of this equation contains a multiple characteristics operator. All conditions are expressed only by the properties of the operators of the given equation.

Article information

Source
Taiwanese J. Math., Volume 15, Number 4 (2011), 1637-1650.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406369

Digital Object Identifier
doi:10.11650/twjm/1500406369

Mathematical Reviews number (MathSciNet)
MR2848979

Zentralblatt MATH identifier
1237.34111

Subjects
Primary: 39B42: Matrix and operator equations [See also 47Jxx] 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

Keywords
operator-differential equation Hilbert space normal solvability multiple characteristics

Citation

Mirzoev, Sabir S.; Humbataliev, Rovshan Z. On Normal Solvability of Boundary Value Problems for Operator-differential Equations on Semi-axis in Weight Space. Taiwanese J. Math. 15 (2011), no. 4, 1637--1650. doi:10.11650/twjm/1500406369. https://projecteuclid.org/euclid.twjm/1500406369


Export citation

References

  • Yu. A. Ustinov and Yu. I. Yudovich, On completeness of a system of elementary solutions of a biharmonic equation on a semi-strip, PMM, 37(4) (1973), 706-714, (in Russian).
  • P. F. Papkovich, Two problems of bend theory of thin elastic plates, PMM, 5(3) (1941), 359-374, (in Russian).
  • P. F. Papkovich, On a form of solution of plane problem of elasticity theory for a rectangular strip, Dokl. AN SSSR, 27(4) (1940), in Russian.
  • A. G. Kostyuchenko and M. B. Orazov, A problem on vibration of an elastic semicylinder and related quadratic bundles. Proceedings of I. G. Petrovsky, seminar, MGU, 6 (1981), 97-146, (in Russian).
  • M. B. Orazov, On completeness of elementary solutions for some operator-differential equations on a semi-axis and segment, DAN SSSR, 245(4) (1979), 788-792, (in Russian).
  • I. I. Vorovich, Some mathematical problems of theory of plates and shells, Procedings of the II All-Union congress on theoretical and applied mechanics, M(3) (1966), 116-136, (in Russian).
  • I. I. Vorovich and B. A. Babenko, Dynamical mixed problems of elasticity theory for nonplastic domains, M., Nauka, (1979), (in Russian).
  • I. I. Vorovich and V. E. Kovalchuk, On basis properties of a system of homogeneous solutions (a problem of elasticity theory for a rectangle), PMM, 31(5) (1967), 861-869, (in Russian).
  • V. E. Kovalchuk, On behavior of the solution of the first basic problem of elasticity theory for a long rectangular plate, PMM, 33(3) (1969), 511-518, (in Russian).
  • A. G. Kostyuchenko and A. A. Shkalikov, Self-adjoint quadratic bundles of operators and elliptic problems, Funk. analiz i ego prilozheniya, 17(2) (1983), 38-61, (in Russian).
  • M. G. Krein and G. K. Langer, On some mathematical principles of theory of damped vibrations of continua, Proceedings of International Sympozium on application of theory of functions of complex variable in continuum mechanics. M., Nauka, 1965, pp. 283-322, (in Russian).
  • S. S. Mirzoev, On conditions of correct solvability of boundary value problems for operator-differential equations, DAN SSSR, 273(2) (1983), 292-295, (in Russian).
  • J. L. Lions and E. Magenes, Inhomogeneous boundary value problems and their applications, Moskwa, Mir, 371 (1971), 371, (in Russian).
  • M. G. Gasymov, To the theory of polynomial operator bundles, DAN SSSR, 199(4) (1971), 747-750, (in Russian).
  • M. G. Gasymov and S. S. Mirzoev, On solvability of boundary value problems for elliptic type operator-differential equations of second order, Different. uravnenie, 28(4) (1992), 651-661, (in Russian).
  • Yu. A. Dubinski, Mixed problems for some classes of partial differential equations, XV (1969), 205-240, (in Russian).
  • A. A. Shkalikov, Elliptic equations in Hilbert space and related spectral problems, Proceedings of I. G. Petrovsky seminar, 14 (1989), 140-224, (in Russian).
  • V. V. Vlasov, On some properties of solutions of a class of evolutionary equations, UMN, 40(5) (1985), 247-248, (in Russian).
  • S. Ya. Yakubov and B. A. Aliev, Fredholm property of a boundary value problem with operator in boundary conditions for a second order elliptic differential-operator equation, DAN SSSR, 257(5) (1981), 1071-1075, (in Russian).
  • V. I. Gorbachuk and M. L. Gorbachuk, Boundary value problems for differential- operator equations, Kiev, Naukova Dumka, 284 (1984), (in Russian).
  • S. S. Mirzoev, On the norms of operators of operators of intermediate derivatives, Transaction of NAS of Azerb., XXIII(1) (2003), 157-164.
  • S. B. Stechkin, The best approximations of linear operators, Matem. zametki, 1(2) (1967), 137-138, (in Russian).
  • L. V. Taykov, Kolmogorov type inequalities and the best formulae of number differentiation, Matem. Zametki, 4(2) (1968), 233-238, (in Russian).
  • G. T. Hardy and Polia G. Littewood, Inequalites. M., \bf (IL) (1948), p. 456.
  • M. G. Gasymov, On solvability of boundary problems for certain class operator-differential equations, DAN SSSR, 235(3) (1977), 505-508, (in Russian).