Skip to main content

Two Dimensional Emden-Fowler Equation with Exponential Nonlinearity

  • Chapter
Nonlinear Diffusion Equations and Their Equilibrium States, 3

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 7))

Abstract

Emden-Fowler equation with the exponential nonlinearity P: arises in the theories of thermonic emission (Gel’fand [10]), isothermal gas sphere (Chandrasekhar [5]), and gas combustion (Mignot-Murat-Puel [17]), where λ is a positive constant and Ω ⊂ R n is a bounded domain with smooth boundary ∂Ω.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Bandle C, Existence theorems, qualitative results and a priori bounds for a class of nonlinear Dirichlet problems, Arch. Rat. Mech. Anal., 58 (1975), 219–238.

    Article  MathSciNet  MATH  Google Scholar 

  2. Bandle C, Isoperimetric inequalities for nonlinear eigenvalue problems, Proc. Amer. Math. Soc, 56 (1976), 243–246.

    Article  MathSciNet  MATH  Google Scholar 

  3. Bandle C, Isoperimetric inequalities and Applications, Pitman, Boston-London-Melbourne, 1980.

    MATH  Google Scholar 

  4. Burago Yu. D. and Zalgaller, V. A., Geometric Inequalities, Springer, Berlin-Heidelberg-New York-London-Paris-Tokyo, 1988.

    MATH  Google Scholar 

  5. Chandrasekhar S., An introduction to the study of Stellar Structure, Chapter 11, Dover, New York, 1957.

    Google Scholar 

  6. Cheng S. Y., Eigenfunctions and nodal sets, Comment. Math. Helvetici, 51 (1976), 43–55.

    Article  MATH  Google Scholar 

  7. Crandall M. G., and Rabinowitz P. H., Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems, Arch. Rat. Mech. Anal., 58 (1975), 207–218.

    Article  MathSciNet  MATH  Google Scholar 

  8. De Figueiredo D. G., Lions P. L., and Nussbaum R. D., A priori estimates and existence of positive solutions of semilinear elliptic equations, J. Math. Pure et Appl., 61 (1982), 41–63.

    MATH  Google Scholar 

  9. Fujita H., On the nolinear equations Δu + e u = 0 andv/∂t = Δt + e v, Bull. Amer. Soc, 75 (1969), 132–135.

    Article  MATH  Google Scholar 

  10. Gel’fand I. M., Some problems in the theory of quasilinear equations, Amer. Math. Soc. Transl., 29(2) (1963), 295–381.

    MathSciNet  Google Scholar 

  11. Gidas B., Ni W. M., and Nirenberg L., Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68 (1979), 209–243.

    Article  MathSciNet  MATH  Google Scholar 

  12. Kenner J. P. and Keller H. B., Positive solutions of convex nonlinear eigenvalue problem, J. Diff. Equat., 16 (1974), 103–125.

    Article  Google Scholar 

  13. Keller H. B. and Cohen D. S., Some positive problems suggested by nonlinear heat generation, J. Math. Mech., 16 (1967), 1361–1376.

    MathSciNet  MATH  Google Scholar 

  14. Laetsch T., On the number of solutions of boundary value problems with convex nonlinearities, J. Math. Anal. Appl., 35 (1971), 389–404.

    Article  MathSciNet  MATH  Google Scholar 

  15. Lin S. S., On non-radially symmetric bifurcation in the annulus, J. Diff. Equat., 80 (1989), 251–279.

    Article  MATH  Google Scholar 

  16. Liouville J., Sur l’équation aux différences partielles2 logλ/∂uv ± λ/2a 2 = 0, J. Math., 18(1853), 71–72.

    Google Scholar 

  17. Mignot F., Murat F. and Puel, J. P., Variation d’un point retourment par rapport au domaine, Comm. P. D. E., 4(1979), 1263–1297.

    Article  MathSciNet  MATH  Google Scholar 

  18. Moseley J. L., Asymptotic solutions for a Dirichlet problem with an exponential nonlinearity, SIAM J. Math. Anal., 14 (1983), 719–735.

    Article  MathSciNet  MATH  Google Scholar 

  19. Nagasaki K. and Suzuki T., Radial and nonradial solutions for the nonlinear eigenvalue problem Δu + λe u =0 on annuli in R 2, J. Diff. Equat., 87 (1990), 144–168.

    Article  MathSciNet  MATH  Google Scholar 

  20. Nagasaki K. and Suzuki T., Asymptotic analysis for two-dimensional elliptic eigenvalue problems with exponentially-dominated nonlinearities, Asymptotic Analysis, 3 (1990), 173–188.

    MathSciNet  MATH  Google Scholar 

  21. Pleijel Å, Remarks on Courant’s nodal line theorem, Comm. Pure Appl. Math., 9 (1956), 543–550.

    Article  MathSciNet  MATH  Google Scholar 

  22. Suzuki T., Radial and nonradial solutions for semilinear elliptic equations, In: Talenti, G. et. al. (eds.), Geometry of Solutions of Partial Differential Equations, Symposia Mathematics bf 30 (1989), Academic Press, pp. 153–174.

    Google Scholar 

  23. Suzuki, T. and Nagasaki K., On the nonlinear eigenvalue problem Δu+ λe u = 0, Trans. Amer. Math. Soc, 309 (1988), 591–608.

    MathSciNet  MATH  Google Scholar 

  24. Weston V. H., On the asymptotic solution of a partial differential equation with an exponential nonlinearity, SIAM J. Math. Anal., 9(1978), 1030–1053.

    Article  MathSciNet  MATH  Google Scholar 

  25. Yamashita S., Derivatives and length-preserving maps, Canad. Math. Bull., 30 (1987), 379–384.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer Science+Business Media New York

About this chapter

Cite this chapter

Suzuki, T. (1992). Two Dimensional Emden-Fowler Equation with Exponential Nonlinearity. In: Lloyd, N.G., Ni, W.M., Peletier, L.A., Serrin, J. (eds) Nonlinear Diffusion Equations and Their Equilibrium States, 3. Progress in Nonlinear Differential Equations and Their Applications, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0393-3_34

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0393-3_34

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6741-6

  • Online ISBN: 978-1-4612-0393-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics