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Dirichlet-Type Problems for Systems of Partial Differential Equations Unresolved with Respect to the Highest Time Derivative

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Abstract

We establish conditions for the correct solvability of problems for systems of partial differential equations unresolved with respect to the highest time derivative with Dirichlet-type conditions with respect to time and periodic conditions with respect to space variables. We prove metric theorems on lower bounds for small denominators appearing in the course of the solution of these problems.

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REFERENCES

  1. N. I. Bilusyak, “Boundary-value problem for differential equations with constant coefficients unresolved with respect to the highest time derivative,” in: Abstracts of the International Scientific Conference “New Approaches to the Solution of Differential Equations” (Drohobych, October 1–5, 2001) [in Ukrainian], Kiev (2001), p. 19.

  2. I. O. Bobyk and B. I. Ptashnyk, “Boundary-value problems for hyperbolic equations with constant coefficients,” Ukr. Mat. Zh., 46, No. 7, 795–802 (1994).

    Google Scholar 

  3. L. I. Komarnyts'ka, “Dirichlet-type problem for systems of differential equations unresolved with respect to the highest time derivative,” in: Abstracts of the International Scientific Conference “New Approaches to the Solution of Differential Equations” (Drohobych, October 1–5, 2001) [in Ukrainian], Kiev (2001), p. 73.

  4. L. I. Komarnyts'ka and B. I. Ptashnyk, “Boundary-value problems for differential equations unresolved with respect to the highest time derivative,” Ukr. Mat. Zh., 47, No. 9, 1197–1208 (1995).

    Google Scholar 

  5. B. I. Ptashnik, “Dirichlet-type problem for systems of hyperbolic equations with constant coefficients,” Mat. Met. Fiz.-Mekh. Polya, Issue 2, 18–23 (1975).

  6. B. I. Ptashnik, Ill-Posed Boundary-Value Problems for Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  7. D. K. Faddeev and I. S. Somins'kyi, Book of Problems in Higher Algebra [in Ukrainian], Vyshcha Shkola, Kiev (1971).

    Google Scholar 

  8. M. A. Naimark, Linear Differential Operators [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  9. A. G. Kurosh, A Course in Highest Algebra [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  10. V. G. Sprindzhuk, Metric Theory of Diophantine Approximations [in Russian], Nauka, Moscow (1977).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, Lviv

    N. I. Bilusyak & B. I. Ptashnyk

  2. Drohobych Pedagogic University, Drohobych

    L. I. Komarnyts'ka

Authors
  1. N. I. Bilusyak
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  2. L. I. Komarnyts'ka
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  3. B. I. Ptashnyk
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Bilusyak, N.I., Komarnyts'ka, L.I. & Ptashnyk, B.I. Dirichlet-Type Problems for Systems of Partial Differential Equations Unresolved with Respect to the Highest Time Derivative. Ukrainian Mathematical Journal 54, 1930–1942 (2002). https://doi.org/10.1023/A:1024065029561

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