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Asymptotics for a sobolev type equation with a critical nonlinearity

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References

  1. Gabov, S.A. and Sveshnikov, A.G., Lineinye zadachi teorii nestatsionarnykh vnutrennikh voln (Linear Problems in the Theory of Nonstationary Internal Waves), Moscow: Nauka, 1990.

    Google Scholar 

  2. Korpusov, M.O. and Sveshnikov, A.G., Zh. Vychisl. Mat. Mat. Fiz., 2003, vol. 43, no. 12, pp. 1835–1869.

    MATH  Google Scholar 

  3. Sobolev, S.L., Izv. Akad. Nauk SSSR. Ser. Mat., 1954, vol. 18, pp. 3–50.

    Google Scholar 

  4. Kaikina, E.I., Naumkin, P.I., and Shishmarev, I.A., Izv. Ross. Akad. Nauk Ser. Mat., 2004, vol. 69, no. 1, pp. 61–114.

    Google Scholar 

  5. Nishihara, K. and Zhao, H., J. Math. Anal. Appl., 2006, vol. 313, no. 2, pp. 598–610.

    Article  MATH  Google Scholar 

  6. Hayashi, N. and Naumkin, P.I., Acta Mathematica Sinica. English Series, 2006, vol. 23, pp. 1–11.

    Google Scholar 

  7. Karch, G., Mathematical Methods in the Applied Sciences, 1997, vol. 20, pp. 271–289.

    Article  MATH  Google Scholar 

  8. Mei, M. and Schmeiser, C., Funkcial. Ekvac., 2001, vol. 44, pp. 151–170.

    MATH  Google Scholar 

  9. Prado, R. and Zuazua, E., Differ. and Integr. Equat., 2002, vol. 15, no. 12, pp. 1409–1434.

    MATH  Google Scholar 

  10. Shishmarev, I.A., Differ. Uravn., 2005, vol. 41, no. 1, pp. 138–140.

    Google Scholar 

  11. Zhang, L., Nonlinear Analisis T.M.A., 1995, vol. 25, pp. 1343–1369.

    Article  MATH  Google Scholar 

  12. Galaktionov, V.A., Kurdyumov, S.P., and Samarskii, A.A., Mat. Sb., 1985, vol. 126, no. 4, pp. 435–472.

    Google Scholar 

  13. Escobedo, M., Kavian, O., and Matano, H., Comm. Partial Differ. Equat., 1994, vol. 20, pp. 1427–1452.

    Article  Google Scholar 

  14. Gmira, A. and Veron, L., J. Differ. Equat., 1984, vol. 53, pp. 258–276.

    Article  MATH  Google Scholar 

  15. Schonbek, M.E., in Advances in Geometric Analysis and Continuum Mechanics (Stanford, CA, 1993), Cambridge, MA, 1995, pp. 269–274.

  16. Zuazua, E., J. Differ. Equat., 1994, vol. 108, pp. 1–35.

    Article  MATH  Google Scholar 

  17. Titchmarsh, E.C., Introduction to the Theory of Fourier Integrals, Oxford: Oxford Univ. Press, 1938. Translated under the title Vvedenie v teoriyu integralov Fur’e, Moscow: Mir, 1944.

    Google Scholar 

  18. Watson, G.N., A Treatise on the Theory of Bessel Functions, Cambridge: Cambridge Univ. Press, 1944. Translated under the title Teoriya funktsii Besselya, Moscow: Inostrannaya Literatura, 1949.

    MATH  Google Scholar 

  19. Naumkin, P.I. and Shishmarev, I.A., Nonlinear Nonlocal Equations in the Theory of Waves, Providence: AMS, 1994, vol. 133.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    E. I. Kaikina, P. I. Naumkin & I. A. Shishmarev

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  1. E. I. Kaikina
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  2. P. I. Naumkin
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  3. I. A. Shishmarev
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Additional information

Original Russian Text © E.I. Kaikina, P.I. Naumkin, I.A. Shishmarev, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 5, pp. 655–668.

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Kaikina, E.I., Naumkin, P.I. & Shishmarev, I.A. Asymptotics for a sobolev type equation with a critical nonlinearity. Diff Equat 43, 673–687 (2007). https://doi.org/10.1134/S0012266107050114

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  • DOI: https://doi.org/10.1134/S0012266107050114

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