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S-shaped bifurcation curves. (English) Zbl 0458.35036

35J65Nonlinear boundary value problems for linear elliptic equations
34B15Nonlinear boundary value problems for ODE
34G20Nonlinear ODE in abstract spaces
35B32Bifurcation (PDE)
Full Text: DOI
[1] Keller, H. B.; Cohen, D. S.: Some positone problems suggested by nonlinear heat generation. J. math. Mech. 16, 1361-1376 (1967) · Zbl 0152.10401
[2] Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM rev. 18, 620-709 (1976) · Zbl 0345.47044
[3] Rabinowitz, P. H.: Some global results for nonlinear eigenvalue problems. J. funct. Anal. 7, 487-513 (1971) · Zbl 0212.16504
[4] Cohen, D. S.; Laetsch, T. W.: Nonlinear boundary value problems suggested by chemical reactor theory. J. diff. Eqns 7, 217-226 (1970) · Zbl 0201.43102
[5] Crandall, M. G.; Rabinowitz, P. H.: Some continuation and variational methods for positive solutions of nonlinear elliptic boundary value problems. Archs. ration. Mech. analysis 58, 207-218 (1975) · Zbl 0309.35057
[6] Crandall, M. G.; Rabinowitz, P. H.: Bifurcation, perturbation of simple eigenvalues and linearized stability. Archs. ration. Mech. analysis 52, 161-180 (1973) · Zbl 0275.47044
[7] Parks, J. R.: Criticality criteria for various configurations of a self-heating chemical as functions of activation energy and temperature of assembly. J. chem. Phys. 34, 46-50 (1961)
[8] Sattinger, D. H.: A nonlinear parabolic system in the theory of combustion. Q. appl. Math. 33, 47-61 (1975) · Zbl 0315.35008
[9] Parter, S. V.: Solutions of a differential equation arising in chemical reactor processes. SIAM J. Appl. math. 26, 687-716 (1974) · Zbl 0285.34013
[10] Tam, K. K.: Construction of upper and lower solutions for a problem in combustion theory. J. math. Analysis applic. 69, 131-145 (1979) · Zbl 0414.35011
[11] Aris, R.: On stability criteria of chemical reaction engineering. Chem. engng. Sci. 24, 149-169 (1969)
[12] Amann, H.: Existence of multiple solutions for nonlinear elliptic boundary value problems. Indiana univ. Math. J. 21, 925-935 (1972) · Zbl 0222.35023
[13] Williams, L. R.; Leggett, R. W.: Multiple fixed point theorems for problems in chemical reactor theory. J. math. Analysis applic. 69, 180-193 (1979) · Zbl 0416.47026
[14] Kernevez, J. P.; Joly, G.; Duban, M. C.; Bunow, B.; Thomas, D.: Hysteresis, oscillations and pattern formation in realistic immobilized enzyme systems. J. math. Biol. 7, 41-56 (1979) · Zbl 0433.92014
[15] Laetsch, T. W.: The number of solutions of a nonlinear two point boundary value problem. Indiana univ. Math. J. 20, 1-13 (1970/1971) · Zbl 0215.14602
[16] Smoller J. & Wasserman A., Global bifurcation of steady state solutions (to appear). · Zbl 0425.34028
[17] Bony, J. M.: Principe de maximum dans LES espaces de Sobolev. CR acad. Sci. Paris sér. 265, 333-336 (1967) · Zbl 0164.16803
[18] Amann, H.; Crandall, M. G.: On some existence theorems for semi-linear elliptic equations. Indiana univ. Math. J. 27, No. No. 5, 779-790 (1978) · Zbl 0391.35030