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Linear boundary-value problems described by Drazin invertible operators

  • Volume 101, Number 6, June, 2017
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Abstract

The main subject of this paper is the study of a general linear boundary-value problem with Drazin or right Drazin (respectively, left Drazin) invertible operators corresponding to initial boundary operators. The obtained results are then employed to solve a Schro¨ dinger equation.

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References

  1. J. Behrndt and M. Langer, “Boundary-value problems for elliptic partial differential operators on bounded domains,” J. Funct. Anal. 243, 536–565 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Behrndt and M. Langer, “Elliptic operators, Dirichlet-to-Neumann maps and quasi-boundary triples,” London Math. Soc. Lecture Note Series 404, 121–160 (2012).

    MathSciNet  MATH  Google Scholar 

  3. J. Behrndt, M. Langer, and V. Lotoreichik, “Trace formulae and singular values of resolvent power differences of self-adjoint elliptic operators,” J. London Math. Soc. 88 (2), 319–337 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  4. P. L. Butzer and J. J. Koliha, “The a-Drazin inverse and ergodic behaviour of semigroups and cosine operator functions,” J. Operator Theory 62 (2), 297–326 (2009).

    MathSciNet  MATH  Google Scholar 

  5. S. L. Campbell, C. D. Meyer, and N. J. Rose, “Application of the Drazin inverse to linear systems of differential aquations with singular constant coefficients,” SIAM J. Appl. Math. 31 (3), 411–425 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  6. M. P. Drazin, “Pseudo-inverse in associative rings and semigroups,” Amer. Math. Monthly 65, 506–514 (1958).

    Article  MathSciNet  MATH  Google Scholar 

  7. N. Khaldi, M. Benharrat, and B. Messirdi, “On the Spectral Boundary Value Problems and Boundary Approximate Controllability of Linear Systems,” Rend. Circ. Mat. Palermo 63, 141–153 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  8. N. Khaldi, M. Benharrat, and B. Messirdi, “Spectral approach for solving boundary value matrix problems: existence, uniqueness and application to symplectic elasticity,” J. Adv. Res. Appl. Math. 6 (4), 68–80 (2014).

    Article  MathSciNet  Google Scholar 

  9. J. J. Koliha and T. D. Tran, The Drazin Inverse for Closed Linear Operators, Preprint, 1998.

    MATH  Google Scholar 

  10. J. J. Koliha and T. D. Tran, “Closed semistable operators and singular differential equations,” Czechoslovak Math. J, 53 (3), 605–620 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  11. J. J. Koliha and Trung Dinh Tran, “The Drazin inverse for closed linear operators and the asymptotic convergence of C0-semigroups,” J. Operator theory 46, 323–336 (2001).

    MathSciNet  MATH  Google Scholar 

  12. M. Z. Nashed and Y. Zhao, “The Drazin inverse for singular evolution equations and paratial differential operators,” World Sci. Ser. Appl. Anal. 1, 441–456 (1992).

    MATH  Google Scholar 

  13. N. V. Mau, Boundary-Value Problems and Controllability of Linear Systems with Right Invertible Operators (DissertationesMath., Warszawa, 1992).

    MATH  Google Scholar 

  14. D. Przeworska-Rolewicz, Algebraic Theory of Right Invertible Operators, Studia Math. XLVIII, 129–144 (1973).

    MathSciNet  MATH  Google Scholar 

  15. V. Ryzhov, “Spectral Boundary Value Problems and their Linear Operators,” Opuscula Mathematica 27 (2), 305–331 (2007).

    MathSciNet  MATH  Google Scholar 

  16. V. Ryzhov, “A Note on an Operator-Theoretic Approach to Classic Boundary Value Problems for Harmonic and Analytic Functions in Complex Plane Domains,” Integr. Equ. Oper. Theory 67, 327–339 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  17. H. V. Thi, “Approximate controllability for systems described by right invertible operators,” Control and Cybernetics 37 (1), 39–51 (2008).

    MathSciNet  MATH  Google Scholar 

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Correspondence to N. Khaldi.

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Khaldi, N., Benharrat, M. & Messirdi, B. Linear boundary-value problems described by Drazin invertible operators. Math Notes 101, 994–999 (2017). https://doi.org/10.1134/S0001434617050261

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  • DOI: https://doi.org/10.1134/S0001434617050261

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