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.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-25002-6_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25001-9
Online ISBN: 978-3-642-25002-6
eBook Packages: Computer ScienceComputer Science (R0)