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The behavior of solutions of semilinear elliptic equations of second order of the form Lu = e u in the infinite cylinder

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We consider a semilinear elliptic equation of second order with variable coefficients of the form Lu = e u in the semi-infinite cylinder whose solution satisfies a homogeneous Neumann condition on the lateral surface of the cylinder.

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References

  1. V. A. Kondrat’ev and O. A. Oleinik, “On the asymptotics of solutions of nonlinear elliptic equations,” International Seminar “Differential Equations and Related Questions” (15th joint session of the Petrovskii Seminar and Moscow Mathematical Society, 19–22 January, 1993), Uspekhi Mat. Nauk 48(4), 184–185 (1993)

    Google Scholar 

  2. O. A. Oleinik, Some Asymptotic Problems of the Theory of Partial Differential Equations, in Lezioni Lincei (Cambridge, Cambridge Univ. Press, 1995).

    Google Scholar 

  3. A. I. Nasrullaev, “Asymptotics of solutions of Neumann’s problem for the equation Δue u = 0 in a semiinfinite cylinder,” Uspekhi Mat. Nauk 50(3), 161–162 (1995) [Russian Math. Surveys 50 (3), 630–632 (1995)].

    MathSciNet  Google Scholar 

  4. O. A. Oleinik, “On the equation Δu + k(x)e u = 0,” Uspekhi Mat. Nauk 33(2), 203–204 (1978) [Russian Math. Surveys 33 (2), 243–244 (1978)].

    Google Scholar 

  5. A. I. Nasrullaev, “On a class of nonlinear equations in unbounded domains,” International Seminar “Differential Equations and Related Questions” (18th joint session of the Petrovskii Seminar and Moscow Mathematical Society, 25–29 January, 1993), UspekhiMat. Nauk 51(5), 160–161 (1996)

    Google Scholar 

  6. O. A. Oleinik and G. A. Iosif’yan, “The behavior at infinity of the solutions of second-order elliptic equations in domains with a noncompact boundary,” Mat. Sb. 112(4), 588–610 (1980).

    MathSciNet  Google Scholar 

  7. A. V. Neklyudov, “On the Neumann problem for higher-order divergent elliptic equations in an unbounded domain, close to a cylinder,” Tr. Semin. Im. I. G. Petrovskogo 16, 191–217 (1991) [J. Math. Sci. (New York) 69 (3), 1072–1091 (1991)].

    Google Scholar 

  8. E.M. Landis and A. I. Ibragimov, “Neumann problems in unbounded domains,” Dokl. Ross. Akad. Nauk 343(1), 17–18 (1995) [Russian Acad. Sci. Dokl.Math. 52 (1), 11–12 (1995)].

    MathSciNet  Google Scholar 

  9. S. S. Lakhturov, “Asymptotic behavior of the solutions of the second boundary-value problem in unbounded domains,” Uspekhi Mat. Nauk 35(4), 195–196 (1980) [Russian Math. Surveys 35 (4), 175–176 (1980)].

    MATH  MathSciNet  Google Scholar 

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Original Russian Text © A. V. Neklyudov, 2009, published in Matematicheskie Zametki, 2009, Vol. 85, No. 3, pp. 408–420.

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Neklyudov, A.V. The behavior of solutions of semilinear elliptic equations of second order of the form Lu = e u in the infinite cylinder. Math Notes 85, 397–408 (2009). https://doi.org/10.1134/S0001434609030109

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