Skip to main content
Log in

Maximum principles and nonlinear elliptic problems

  • Published:
Journal d’Analyse Mathématique Aims and scope

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. H. Amann,Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. (18)4 (1976), 620–709.

    Article  MathSciNet  Google Scholar 

  2. C. Bandle,Bounds for the solution of Poisson problems and applications to nonlinear eigenvalue problems, SIAM J. Math. Anal.6 (1975), 146–152.

    Article  MATH  MathSciNet  Google Scholar 

  3. C. Bandle and J. Hersch,Problèmes de Dirichlet nonlinéaires: une condition suffisante isopérimétrique pour l'éxistence d'une solution, C.R. Acad. Sci. ParisA28 (1975), 1057–1060.

    MathSciNet  Google Scholar 

  4. E. Hopf,A remark on linear elliptic differential equations of the second order, Proc. Amer. Math. Soc.3 (1952), 791–793.

    Article  MATH  MathSciNet  Google Scholar 

  5. S. I. Hudjaev,Boundary value problems for certain quasilinear elliptic equations, Soviet Math.5 (1964), 188–192.

    Google Scholar 

  6. T. Laetsch,The number of solutions of a nonlinear two point boundary value problem, Indiana Univ. Math. J.20 (1970), 1–13.

    Article  MATH  MathSciNet  Google Scholar 

  7. C. Miranda,Formule di maggiorazione e teorem di esistenza per le funzioni biarmoniche de due variabili, Giron. Math. Battaglini78 (1948–49), 97–118.

    MathSciNet  Google Scholar 

  8. Z. Opial,Sur les périodes des solutions de l'équation différentiell x″+g(x)=0, Ann. Polon. Math.10 (1961), 49–72.

    MATH  MathSciNet  Google Scholar 

  9. L. E. Payne,Bounds for the maximum stress in the Saint Venant torsion problem, Indian J. Mech. Math., Special Issue (1968), 51–59.

  10. L. E. Payne,Some remarks on maximum principles, J. Analyse Math.30 (1976), 421–433.

    Article  MATH  MathSciNet  Google Scholar 

  11. L. E. Payne and G. Philippin,Some applications of the maximum principle in the problem of torsional creep, SIAM J. Appl. Math.33 (1977), 446–455.

    Article  MATH  MathSciNet  Google Scholar 

  12. L. E. Payne and I. Stakgold,Nonlinear problems in nuclear reactor analysis, Proc. Conf. on Nonlinear Problems in Physical Sciences and Biology, Springer Lecture Notes in Math.322, 1972, pp. 298–307.

  13. L. E. Payne, I. Stakgold and R. P. Sperb,On Hopftype maximum principles for convex domains, Nonlinear Analysis1 (1977), 547–559.

    Article  MATH  MathSciNet  Google Scholar 

  14. M. H. Protter and H. F. Weinberger,A maximum principle and gradient bounds for linear elliptic equations, Indiana Univ. Math. J.23 (1973), 239–249.

    Article  MATH  MathSciNet  Google Scholar 

  15. D. H. Sattinger,Topics in stability and bifurcation theory, Springer Lecture Notes in Math.309, 1973.

  16. P. W. Schaefer and R. P. Sperb,Maximum principles for some functionals associated with the solution of elliptic boundary value problems, Arch. Rational Mech. Anal.61 (1976), 65–76.

    Article  MATH  MathSciNet  Google Scholar 

  17. P. W. Schaefer and R. P. Sperb,Maximum principles and bounds in some inhomogeneous elliptic boundary value problem, SIAM J. Math. Anal.8 (1977), 871–878.

    Article  MATH  MathSciNet  Google Scholar 

  18. R. P. Sperb,Growth estimates in reaction-diffusion problems, to be published in Arch. Rat. Mech. Anal. (1979).

  19. C. E. Weatherburn,Differential Geometry in Three Dimensions, Vol. 2, Cambridge Univ. Press, 1930.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Present address: Techn. chem. Laboratorium ETHZ, CH-8092 Zurich, Switzerland.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sperb, R.P. Maximum principles and nonlinear elliptic problems. J. Anal. Math. 35, 236–263 (1979). https://doi.org/10.1007/BF02791067

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02791067

Keywords

Navigation