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On the Oscillation Properties of Elliptic Equations in Unbounded Domains

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Abstract

For the equation \((-\Delta )^{m}U+a(x)U=0 \), where \(\Delta \) is the Laplace operator, with a measurable locally bounded coefficient \( a(x)\), we give the oscillation and nonoscillation criteria in an unbounded domain that can be narrowing or expanding in a certain way at infinity.

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REFERENCES

  1. Allegretto, W., Nonoscillation criteria for elliptic equations in conical domains, Proc. Am. Math. Soc., 1977, vol. 63, pp. 245–250.

    Article  MathSciNet  MATH  Google Scholar 

  2. Swanson, C., Comparison theorems for elliptic equations on unbounded domains, Trans. Am. Math. Soc., 1967, vol. 126, pp. 278–285.

    Article  MathSciNet  MATH  Google Scholar 

  3. Swanson, C., Strong oscillation on elliptic equations in general domain, Can. Math. Bull., 1970, vol. 16, pp. 105–110.

    Article  MathSciNet  Google Scholar 

  4. Headley, B. and Swanson, C.A., Oscillation criteria for elliptic equations, Pac. J. Math., 1968, vol. 27, pp. 501–506.

    Article  MathSciNet  MATH  Google Scholar 

  5. Kreith, K., Comparison theorems for general elliptic equations with mixed boundary, J. Differ. Equat., 1970, vol. 8, pp. 537–541.

    Article  MathSciNet  MATH  Google Scholar 

  6. Toraev, A., Ostsillyatsionnye svoistva reshenii ellipticheskikh uravnenii (Oscillation Properties of Solutions of Elliptic Equations), Ashkhabad: Ylym, 1985.

    Google Scholar 

  7. Toraev, A., On oscillation and nonoscillation of solutions of elliptic equations, Differ. Uravn., 1986, vol. 22, no. 8, pp. 1424–1435.

    MathSciNet  Google Scholar 

  8. Egorov, Yu.V. and Kondrat’ev, V.A., On the negative spectrum of an elliptic operator, Sb. Math., 1991, vol. 69, no. 1, pp. 155–177.

    Article  MathSciNet  MATH  Google Scholar 

  9. Mikhlin, S.G., Lineinye uravneniya v chastnykh proizvodnykh (Linear Partial Differential Equations), Moscow: Vyssh. Shkola, 1984.

    Google Scholar 

  10. Kantorovich, L.V. and Akilov, G.P., Funktsional’nyi analiz (Functional Analysis), Moscow: Nauka, 1984.

    Google Scholar 

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ACKNOWLEDGMENTS

The author expresses his deep gratitude to the reviewer of the article for valuable comments.

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Authors and Affiliations

  1. Turkmen State Institute of Architecture and Construction, Ashgabat, 744000, Turkmenistan

    A. Toraev

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  1. A. Toraev
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Correspondence to A. Toraev.

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Translated by V. Potapchouck

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Toraev, A. On the Oscillation Properties of Elliptic Equations in Unbounded Domains. Diff Equat 58, 1432–1437 (2022). https://doi.org/10.1134/S00122661220100123

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  • DOI: https://doi.org/10.1134/S00122661220100123

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