An application of the invariance principle to reaction diffusion equations. (English) Zbl 0386.34046


34D20 Stability of solutions to ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
Full Text: DOI


[1] J. F. G. Auchmuty, ”Qualitative Effects of Diffusion in Chemical Systems,” Lectures on Mathematics in the Life Sciences, in press. · Zbl 0411.76063
[2] Chafee, N.; Infante, E.: A bifurcation problem for a nonlinear parabolic equation. Applicable anal., 74-75 (1974) · Zbl 0296.35046
[3] Williams, S.; Chow, P. L.: Nonlinear reaction-diffusion models. J. math. Anal. appl. 62, 157-169 (1978) · Zbl 0372.35047
[4] Dafermos, C. M.: An invariance principle for compact processes. J. differential equations 9, 239-252 (1971) · Zbl 0236.34038
[5] Friedman, A.: Partial differential equations of parabolic type. (1964) · Zbl 0144.34903
[6] Friedman, A.: Partial differential equations. (1969) · Zbl 0224.35002
[7] Gagliardo, C.: Ulteriori propzietoi di allnno classi di funzioni in piu variabili. Ricerch mat. 8, 24-51 (1959) · Zbl 0199.44701
[8] Glushko, V. P.; Krein, S. G.: Fractional powers of differential operators and embedding theorems. Dokl. akad. Nauk. SSSR 122, 963-966 (1958) · Zbl 0089.32503
[9] Hale, J. K.: Ordinary differential equations. (1969) · Zbl 0186.40901
[10] Hale, J. K.: Dynamical systems and stability. J. math. Anal. appl. 26, 39-59 (1969) · Zbl 0179.13303
[11] Hale, J. K.; Stokes, A. P.: Behavior of solutions near integral manifolds. Arch. rational mech. Anal. 16 (1960) · Zbl 0093.08903
[12] D. Henry, ”Geometric Theory of Semilinear Parabolic Equations,” monograph, University of Kentucky, Lexington, in press. · Zbl 0456.35001
[13] Hille, E.; Phillips, R. S.: Functional analysis and semigroups. Amer. math. Soc. colloquium publ. 31 (1954)
[14] Iooss, G.: Existence et stabilité de la solution peridique secondaize intervenant dans LES problème d’évolution du type Navier-Stokes. Arch. rational mech. Anal. (1973)
[15] Ladyzenskaya, O. A.; Ural’ceva, N. N.: Linear and quasilinear elliptic equations. (1968)
[16] Ladyzenskaya, O. A.; Solonnikov, V. A.; Ural’ceva, N. N.: Linear and quasilinear equations of parabolic type. Amer. math. Soc. trans. 23 (1968)
[17] Lasalle, J. P.: Stability theory and the asumptotic behavior of dynamical systems. Dynamic stability of structures, proc. International conference (1966)
[18] Marsden, J. E.; Mccraken, M.: The Hopf bifurcation and its applications. (1976)
[19] Mallet-Paret, J.: Negatively invariant sets of compact maps and an extension of a theorem of cartwright. J. differential equations (1976) · Zbl 0354.34072
[20] Protter, M. H.; Weinberger, H. F.: Maximum principles in differential equations. (1967) · Zbl 0153.13602
[21] Smale, S.; Hirch, M.: Dynamical systems and linear algebra. (1975)
[22] M. R. May, ”Stability and Complexity in Model E cosystems,” Princeton Univ. Press, Princeton, N.J.
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.