Archive for Rational Mechanics and Analysis

, Volume 112, Issue 4, pp 319–338 | Cite as

On positive solutions of emden equations in cone-like domains

  • Catherine Bandle
  • Matts Essén


Dirichlet Boundary Condition Regular Solution Singular Solution Positive Radial Solution Emden Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [A]
    V. S. Azarin,Generalization of a theorem of Hayman on subharmonic functions in an n-dimensional cone, AMS Transl. (2)80 (1969), 119–138. Math. USSR Sb.66 (108), (1965), 248–264.zbMATHGoogle Scholar
  2. [BL]
    C. Bandle &H. A. Levine,On the existence and nonexistence of global solutions of reaction diffusion equations in sectorial domains, Trans. Amer. Math. Soc.314 (1989), 595–622.CrossRefMathSciNetGoogle Scholar
  3. [BM]
    C. Bandle &M. Marcus,On the structure of the positive radial solutions for a class of nonlinear elliptic equations, J. reine angew. Math. (Crelle)401 (1989) 25–59.zbMATHMathSciNetGoogle Scholar
  4. [B]
    G. Bouligand,Sur les fonctions de Green et de Neumann du cylindre, Bull. Soc. Math. France42 (1914), 168–242.MathSciNetGoogle Scholar
  5. [ELe]
    M. Essén &J. L. Lewis,The generalized Ahlfors-Heins theorem in certain d-dimensional cones, Math. Scand.33 (1973), 113–129.zbMATHMathSciNetGoogle Scholar
  6. [EL]
    M. J. Esteban &P. L. Lions,Existence and non-existence results for semilinear elliptic problems in unbounded domains, Proc. Royal Soc. Edinburgh93 A (1982), 1–14.CrossRefMathSciNetGoogle Scholar
  7. [GS]
    B. Gidas &J. Spruck,Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math.34 (1981), 525–598.CrossRefzbMATHMathSciNetGoogle Scholar
  8. [KKO]
    V. A. Kondratev, I. Kopschek &O. A. Oleinik,On the best Hölder exponents for generalized solutions of the Dirichlet problem for a second order elliptic equation, Math. USSR Sb.59 (1988), 113–127.CrossRefMathSciNetGoogle Scholar
  9. [LF]
    J. Lelong-Ferrand,Etudes des fonctions surharmoniques positives dans un cylindre ou dans un cône, C. R. Acad. Sciences (Paris)229 (1949), 340–341.zbMATHMathSciNetGoogle Scholar
  10. [PS]
    P. Pucci &J. Serrin,A general variational identity, Indiana Univ. Math. J.35 (1986), 681–703.CrossRefzbMATHMathSciNetGoogle Scholar
  11. [To]
    P. Tolksdorf,On the Dirichlet problems for quasilinear equations in domains with conical boundary points, Comm. Part. Diff. Equ.8 (7) (1983), 773–817.CrossRefzbMATHMathSciNetGoogle Scholar
  12. [W]
    D. V. Widder,The Laplace Transform, Princeton (1941).Google Scholar
  13. [Wi]
    K.-O. Widman,Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations, Math. Scand.21 (1976), 17–37.MathSciNetGoogle Scholar
  14. [Wo]
    J. S. W. Wong,On the generalized Emden-Fowler equation, SIAM Review17 (1975), 339–360.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Catherine Bandle
    • 1
    • 2
  • Matts Essén
    • 1
    • 2
  1. 1.Mathematisches InstitutUniversität BaselSwitzerland
  2. 2.Department of MathematicsUppsala UniversitySweden

Personalised recommendations