Rothe, Franz Global existence of branches of stationary solutions for a system of reaction diffusion equations from biology. (English) Zbl 0471.35031 Nonlinear Anal., Theory Methods Appl. 5, 487-498 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 16 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35A15 Variational methods applied to PDEs 35B32 Bifurcations in context of PDEs 35B50 Maximum principles in context of PDEs 35J50 Variational methods for elliptic systems Keywords:reaction-diffusion equations; pattern formation; global bifurcation theory; variational method of Ljusternik-Schnirelman; existence of stationary solutions; Dirichlet- or Neumann-boundary condition; maximum principle PDF BibTeX XML Cite \textit{F. Rothe}, Nonlinear Anal., Theory Methods Appl. 5, 487--498 (1981; Zbl 0471.35031) Full Text: DOI References: [1] Amann, H., Existence of multiple solutions for nonlinear elliptic boundary value problems, Indiana Univ. math. J., 21, 925-935 (1972) · Zbl 0222.35023 [2] Conway, E. D.; Smoller, J. A., A comparison technique for systems of reaction-diffusion equations, Comm. part. diff. Eqns, 2, 7, 657-679 (1977) · Zbl 0386.35003 [3] Maginu, K., Reaction-diffusion equations describing morphogenesis. I. Wav́eform stability of stationary wave solutions in one-dimensional model, Math. Biosciences, 27, 17-98 (1975) · Zbl 0337.92003 [4] Meinhardt, H., A model of pattern formation in insect embryogenesis, J. Cell. Sci., 23, 117-139 (1977) [5] De Mottoni, P.; Talenti, G.; Tesei, A., Stability results for a class of nonlinear parabolic equations, Annali Mat. pura appl. Ser. IV, 145, 295-310 (1977) · Zbl 0377.35039 [6] Nicolis, G.; Auchmuty, J. F.G., Bifurcation analysis of nonlinear reaction-diffusion equations. I. Evolution equations and the steady state solutions, Bull. math. Biology, 37, 323-365 (1975) · Zbl 0357.35048 [7] Rabinowitz, P. H., Some aspects of nonlinear eigenvalue problems, Rocky Mountain J. Math., 3, 2, 161-202 (1973) · Zbl 0255.47069 [8] Rabinowitz, P. H., Variational methods for nonlinear eigenvalue problems, (Eigenvalues of Nonlinear Problems (1974), Centro Internat. Math. Estivo (CIME) 3. Circlo Varenna) · Zbl 0212.16504 [9] Rothe, F.; De Mottoni, P., A simple system of reaction-diffusion equations describing morphogenesis. I. Asymptotic behaviour, Annali Mat. pura appl., 122, 4, 141-157 (1979) · Zbl 0425.35017 [10] Rothe, F., Some analytical results about a simple reaction-diffusion system for morphogenesis, J. math. Biol., 7, 375-384 (1979) [12] Turing, A. M., The chemical basis of morphogenesis, Trans. R. Soc., B237, 37-92 (1952) · Zbl 1403.92034 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.