References
Bohl, P., Über die Bewegung eines mechanischen Systems in der Nähe einer Gleichgewichtslage. Journal für Math. 127 (1904).
Browder, F. E., On the Solvability of Nonlinear Functional Equations. Duke Math. J. 30 (1963).
Browder, F. E., Nonlinear Elliptic Boundary Value Problems. Bull. Am. Math. Soc. 69 (1963).
Browder, F. E., Nonlinear Parabolic Boundary Value Problems of Arbitrary order. Bull. Am. Math. Soc. 69 (1963).
Browder, F. E., Variational Boundary Value Problems for Quasi-linear Elliptic Equations of Arbitrary Order. Proc. Nat. Acad. Sci. U.S.A. 50 (1963).
Browder, F. E., Strongly Nonlinear Parabolic Boundary Value Problems. Amer. J. Math. 85 (1964).
Day, M. M., Normed Linear Spaces. Berlin-Göttingen-Heidelberg: Springer 1958.
Dolph, C. L., & G. J. Minty, On Nonlinear Integral Equations of the Hammerstein Type (to appear).
Finn, R., On the Steady-state Solutions of the Navier-Stokes Equations III. Acta Math. 105, 197–244 (1961).
Finn, R., Stationary Solutions of the Navier-Stokes Equations. Proc. Symp. Appl. Math. 19 (1965) AMS.
Fujita, H., & T. Kato, On the Navier-Stokes Initial Value Problem I. Arch. Rational Mech. Anal. 16, 4 (1964).
Ladyzhenskaia, O. A., The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon & Breach 1963.
Minty, G., Monotone (Nonlinear) Operators in Hilbert Space. Duke Math. J. 29 (1962).
Minty, G., On a “Monotonicity” Method for the Solution of Nonlinear Equations in Banach Spaces. Proc. Nat. Acad. Sci. U.S.A. 50 (1963).
Minty, G., Two Theorems on Nonlinear Functional Equations in Hilbert Space. Bull. Am. Math. Soc. 69 (1963).
Poincaré, H., Sur les Courbes Définies par les Equations Différentielles. Journal de Math., Vol. II (1886).
Serrin, J., The Initial Value Problem for the Navier-Stokes Equations. Non-linear Problems. Madison: University of Wisconsin Press 1963.
Shinbrot, M., A Fixed Point Theorem and Some Applications. Arch. Rational Mech. Anal. 17, No. 4 (1964).
Author information
Authors and Affiliations
Additional information
Communicated by R. Finn
This work was sponsored in part by the National Science Foundation Grant No. 2426.
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00253136