Skip to main content
Log in

Quasi-compact non-linear operators in Banach space and applications

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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. Bohl, P., Über die Bewegung eines mechanischen Systems in der Nähe einer Gleichgewichtslage. Journal für Math. 127 (1904).

  2. Browder, F. E., On the Solvability of Nonlinear Functional Equations. Duke Math. J. 30 (1963).

  3. Browder, F. E., Nonlinear Elliptic Boundary Value Problems. Bull. Am. Math. Soc. 69 (1963).

  4. Browder, F. E., Nonlinear Parabolic Boundary Value Problems of Arbitrary order. Bull. Am. Math. Soc. 69 (1963).

  5. Browder, F. E., Variational Boundary Value Problems for Quasi-linear Elliptic Equations of Arbitrary Order. Proc. Nat. Acad. Sci. U.S.A. 50 (1963).

  6. Browder, F. E., Strongly Nonlinear Parabolic Boundary Value Problems. Amer. J. Math. 85 (1964).

  7. Day, M. M., Normed Linear Spaces. Berlin-Göttingen-Heidelberg: Springer 1958.

    Google Scholar 

  8. Dolph, C. L., & G. J. Minty, On Nonlinear Integral Equations of the Hammerstein Type (to appear).

  9. Finn, R., On the Steady-state Solutions of the Navier-Stokes Equations III. Acta Math. 105, 197–244 (1961).

    Google Scholar 

  10. Finn, R., Stationary Solutions of the Navier-Stokes Equations. Proc. Symp. Appl. Math. 19 (1965) AMS.

  11. Fujita, H., & T. Kato, On the Navier-Stokes Initial Value Problem I. Arch. Rational Mech. Anal. 16, 4 (1964).

    Google Scholar 

  12. Ladyzhenskaia, O. A., The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon & Breach 1963.

    Google Scholar 

  13. Minty, G., Monotone (Nonlinear) Operators in Hilbert Space. Duke Math. J. 29 (1962).

  14. Minty, G., On a “Monotonicity” Method for the Solution of Nonlinear Equations in Banach Spaces. Proc. Nat. Acad. Sci. U.S.A. 50 (1963).

  15. Minty, G., Two Theorems on Nonlinear Functional Equations in Hilbert Space. Bull. Am. Math. Soc. 69 (1963).

  16. Poincaré, H., Sur les Courbes Définies par les Equations Différentielles. Journal de Math., Vol. II (1886).

  17. Serrin, J., The Initial Value Problem for the Navier-Stokes Equations. Non-linear Problems. Madison: University of Wisconsin Press 1963.

    Google Scholar 

  18. Shinbrot, M., A Fixed Point Theorem and Some Applications. Arch. Rational Mech. Anal. 17, No. 4 (1964).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by R. Finn

This work was sponsored in part by the National Science Foundation Grant No. 2426.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kaniel, S. Quasi-compact non-linear operators in Banach space and applications. Arch. Rational Mech. Anal. 20, 259–278 (1965). https://doi.org/10.1007/BF00253136

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00253136

Keywords

Navigation