Abstract
Basing on the Karamata regular variation theory and combining with the method of explosive sub and supersolution, we establish the asymptotic behavior of large solutions to a quasilinear elliptic equation type with convection terms. the nonlinear term is Γ −varying at infinity, which variation at infinity is not regular. The results of this paper emphasizes the central role played by the convection term and the weight functions.
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References
Bieberbach, L.: Δu = e u und die automorphen Funktionen. Math. Ann. 77, 173–212 (1916)
Bingham, N.H., Goldie, C.M., Teugels, J.L.: Regular Variation. Cambridge University Press, Cambridge (1987)
Cîrstea, F., Rǎdulescu, V.: Boundary blow-up in nonlinear elliptic equations of Bieberbach-Rademacher type. Trans. Amer. Math. Soc. 359, 3275–3286 (2007)
Guo, Z., Shang, J.: Remarks on uniqueness of boundary blow-up solutions. Nonlinear Anal. 66, 484–497 (2007)
Huang, S., Tian, Q.: Asymptotic behavior of large solutions to p-Laplacian of Bieberbach-Rademacher type. Nonlinear Anal. 71, 5773–5780 (2009)
Liu, C., Yang, Z.: Boundary blow-up quasilinear elliptic problems of the Bieberbach type with nonlinear gradient terms. Nonlinear Anal. 69, 4380–4391 (2008)
Melián, J.: Boundary behavior for large solutions to elliptic equations with singular weights. Nonlinear Anal. 67, 818–826 (2007)
Melián, J.: A remark on the existence of large solutions via sub and supersolutions. Electronic J. Differential Equation 110, 1–4 (2003)
Melián, J., Rossi, J.D., Sabina, J.: Large solutions to the p-Laplacian for large p. Calc. Var. Partial Differ. Equat. 31, 187–204 (2008)
Resnick, S.I.: Extreme Values, Regular Variation, and Point Processes. Springer, Berlin (1987)
Seneta, E.: Regularly Varying Functions. Lecture Notes in Math, vol. 508. Springer, Berlin (1976)
Yu, J., Zhang, z.: On the Existence of Explosive Solutions for Semilinear Elliptic Equations. Mathematica Applicata 12, 4–8 (1999)
Lin, Z., Xie, C., Wang, m.: Blow-up Estimates of Solutions to Semilinear Heat Equations with Nonlinear Boundary Condition. Mathematica Applicata 11, 96–100 (1998)
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Zhao, Y. (2011). Estimate of Large Solution to p-Laplacian Equation of Bieberbach-Rademacher Type with Convection Terms. In: Wu, Y. (eds) High Performance Networking, Computing, and Communication Systems. ICHCC 2011. Communications in Computer and Information Science, vol 163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25002-6_10
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DOI: https://doi.org/10.1007/978-3-642-25002-6_10
Publisher Name: Springer, Berlin, Heidelberg
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