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A Problem with Nonlocal Conditions for Partial Differential Equations with Variable Coefficients

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Abstract

We establish conditions for the unique solvability of a problem for partial differential equations with coefficients dependent on variables t and x in a rectangular domain with nonlocal two-point conditions with respect to t and local boundary conditions with respect to x. We prove metric statements related to lower bounds of small denominators appearing in the course of solution of the problem.

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REFERENCES

  1. T. P. Hoi, “A problem with nonlocal conditions for a partial differential equation perturbed by a nonlinear integro-differential term,” Mat. Stud. Pr. L'viv Mat. Tov., 8, No. 1, 71–78 (1997).

    Google Scholar 

  2. T. P. Hoi and B. I. Ptashnyk, “Nonlocal boundary-value problems for systems of linear partial differential equations with variable coefficients,” Ukr. Mat. Zh., 49, No. 11, 1478–1486 (1997).

    Google Scholar 

  3. N. M. Zadorozhna and B. I. Ptashnyk, “A nonlocal boundary-value problem for parabolic equations with variable coefficients,” Ukr. Mat. Zh., 47, No. 7, 915–921 (1995).

    Google Scholar 

  4. V. S. Il'kiv, V. N. Polishchuk, and B. I. Ptashnik, “A nonlocal boundary-value problem for systems of pseudodifferential equations,” in: Methods for Investigation of Differential and Integral Operators [in Russian], Naukova Dumka, Kiev (1989), pp. 75–79.

    Google Scholar 

  5. V. S. Il'kiv and B. I. Ptashnyk, “Representation and investigation of solutions of a nonlocal boundary-value problem for a system of partial differential equations,” Ukr. Mat. Zh., 48, No. 2, 184–194 (1996).

    Google Scholar 

  6. L. I. Komarnyts'ka, “A nonlocal boundary-value problem for an equation with variable coefficients unsolved with respect to the higher derivative,” Visn. L'viv Univ., Ser. Mekh.-Mat., Issue 40, 17–23 (1994).

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

    Google Scholar 

  8. I. G. Petrovskii, Lectures on Partial Differential Equations [in Russian], Gostekhteorizdat, Moscow (1950).

    Google Scholar 

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

    Google Scholar 

  10. V. P. Mikhailov, Partial Differential Equations [in Russian], Nauka, Moscow (1983).

    Google Scholar 

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Authors and Affiliations

  1. Carpathian University, Ivano-Frankivs'k

    O. D. Vlasii

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

    B. I. Ptashnyk

Authors
  1. O. D. Vlasii
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  2. B. I. Ptashnyk
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Vlasii, O.D., Ptashnyk, B.I. A Problem with Nonlocal Conditions for Partial Differential Equations with Variable Coefficients. Ukrainian Mathematical Journal 53, 1607–1617 (2001). https://doi.org/10.1023/A:1015235708785

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