×

Stability of bifurcating solutions by Leray-Schauder degree. (English) Zbl 0232.34027


MSC:

34G20 Nonlinear differential equations in abstract spaces
47J25 Iterative procedures involving nonlinear operators
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Agmon, S., Lectures on Elliptic Boundary Value Problems. Princeton: Van Nostrand 1965. · Zbl 0142.37401
[2] Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability. Oxford: University Press 1961.
[3] Dunford, N., & J. T. Schwartz, Linear Operators, Part I: General Theory. New York: Interscience 1958. · Zbl 0084.10402
[4] Joseph, D. D., On the stability of the Boussinesq equations. Arch. Rational Mech. Anal. 20, 59–71 (1965). · Zbl 0136.23402
[5] Keller, J. B., & S. Antman, Bifurcation Theory and Nonlinear Eigenvalue Problems. Benjamin 1969. · Zbl 0181.00105
[6] Kirchgässner, K., Die Instabilität der Strömung zwischen zwei rotierenden Zylindern gegenüber Taylor-Wirbeln für beliebige Spältbreiten. Zeit. Ang. Math. Phys. 12 (1961). · Zbl 0101.42902
[7] Kirchgässner, K., & P. Sorger, Stability Analysis of Branching Solutions of the Navier Stokes equations. Proc. of the Twelfth International Congress of Applied Mechanics, Stanford Univ., August, 1968. · Zbl 0191.25304
[8] Leray, J., & J. Schauder, Topologie et Equations Fonctionelles. Ann. Sci. Ecole Norm. Sup. 3, Ser. 51, 45–78 (1934). · JFM 60.0322.02
[9] Moskalev, O. B., Critical conditions for a reactor when the connection between the temperature and the neutron flux is nonlinear. U.S.S.R. Comp. Math. and Math. Phys. 3, no. 2, 430–441 (1963). · Zbl 0138.23402
[10] Rabinowttz, P. H., Existence and nonuniqueness of rectangular solutions of the Bénard problem. Arch. Rational Mech. Anal. 29, 32–57 (1968). · Zbl 0164.28704
[11] Sattinger, D. H., The mathematical problem of hydrodynamic stability. J. Math, and Mech. 19, 797–817 (1970). · Zbl 0198.30401
[12] Sattinger, D. H., Stability of nonlinear hyperbolic equations. Arch. Rational Mech. Anal. 28, 226–244 (1968). · Zbl 0157.17201
[13] Sattinger, D. H., Global solutions of nonlinear hyperbolic equations. Arch. Rational Mech. Anal. 30, 148–172 (1968). · Zbl 0159.39102
[14] Schluter, A., D. Lortz, & F. Busse, On the stability of steady finite amplitude convection. J. Fluid Mech. 23, part 1, 129–144 (1965). · Zbl 0134.21801
[15] Schwartz, J. T., Nonlinear Functional Analysis. Notes, Courant Inst. of Math. Sci. 1965.
[16] Velte, W., Stabilitätsverhalten und Verzweigung stationärer Losungen der Navier-Stokesschen Gleichungen. Arch. Rational Mech. Anal. 16, 97–125 (1964). · Zbl 0131.41808
[17] Velte, W., Stabilität und Verwzeigung stationärer Losungen der Navier-Stokesschen Gleichungen beim Taylorproblem. Arch. Rational Mech. Anal. 22, 1–14 (1966). · Zbl 0233.76054
[18] Yudovich, V. I., On the origin of convection. PMM (Jour. Appl. Math, and Mech.) 30, no. 6, 1193–1199 (1966).
[19] Yudovich, V. I., Free convection and bifurcation. PMM 31, No. 2 (1967). · Zbl 0173.28803
[20] Yudovich, V. I., Stability of convection flows. PMM 31, No. 2, 294–303 (1967). · Zbl 0173.28804
[21] Yudovich, V. I., The bifurcation of a rotating flow of fluid. Dokl. Akad. Nauk USSR 169, no. 2, 306–309.
[22] Dieudonné, J., Foundations of Modern Analysis. New York: Academic Press 1960. · Zbl 0100.04201
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.