One-parameter global bifurcation in a multiparameter problem

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1. [1] Alexander, J. C. and Antman, S. S., Global and local behavior of bifurcating multidimensional continua of solutions for multiparameter nonlinear eigenvalue problems, Arch. Rational Mech. Anal. 76 (1981), 339-354. Zbl0479.58005
2. [2] Alexander, J. C. and Fitzpatrick, P. M., Galerkin approximations in several parameter bifurcation problems, Math. Proc. Cambridge Philos. Soc. 87 (1980), 489-500. Zbl0455.47047
3. [3] Alexander, J. C. and Yorke, J. A., Global bifurcation of periodic orbits, Amer. J. Math. 100 (1978), 263-292. Zbl0386.34040
4. [4] Cantrell, R. S., A homogeneity condition guaranteeing bifurcation in multiparameter nonlinear eigenvalue problems, Nonlinear Anal. 8 (1984), 159-169. Zbl0545.34012
5. [5] Cantrell, Multiparameter bifurcation problems and topological degree, J. Differential Equations 52 (1984), 39-51. Zbl0488.47033
6. [6] Crandall, M. G. and Rabinowitz, P. H., Bifurcation from simple eigenvalues, J. Funct. Anal. 8 (1971), 321-340. Zbl0219.46015
7. [7] Esquinas, J. and López-Gómez, J., Optimal multiplicity in local bifurcation theory. I. Generalized generic eigenvalues, J. Differential Equations 71 (1988), 71-92. Zbl0648.34027
8. [8] Esquinas, J. and López-Gómez, J., Optimal multiplicity in bifurcation theory. II. General case, ibid. 75 (1988), 206-215. Zbl0668.47043
9. [9] Esquinas, J. and López-Gómez, J., Multiparameter bifurcation for some reaction-diffusion systems, Proc. Roy. Soc. Edinburgh Sect. A 112 (1989), 135-143. Zbl0727.35010
10. [10] Fitzpatrick, P. M., Homotopy, linearization and bifurcation, Nonlinear Anal. 12 (1988), 171-184. Zbl0653.58028
11. [11] Fitzpatrick, P. M., Massabó, I. and Pejsachowicz, J., Global several-parameter bifurcation and continuation theorems: a unified approach via complementing maps, Math. Ann. 263 (1983), 61-73. Zbl0519.58024
12. [12] Hale, J. K., Bifurcation from simple eigenvalues for several parameter families, Nonlinear Anal. 2 (1978), 491-497. Zbl0383.34050
13. [13] Ize, J., Bifurcation theory for Fredholm operators, Mem. Amer. Math. Soc. 174 (1976). Zbl0338.47032
14. [14] Ize, J., Necessary and sufficient conditions for multiparameter bifurcation, Rocky Mountain J. Math. 18 (1988), 305-337. Zbl0652.58008
15. [15] Ize, J., Massabó, I., Pejsachowicz, J. and Vignoli, A., Structure and dimension of global branches of solutions to multiparameter nonlinear equations, Trans. Amer. Math. Soc. 291 (1985), 383-435. Zbl0578.58005
16. [16] López-Gómez, J., Multiparameter bifurcation based on the linear part, J. Math. Anal. Appl. 138 (1989), 358-370. Zbl0668.47042
17. [17] Magnus, R. J., A generalization of multiplicity and the problem of bifurcation, Proc. London Math. Soc. 32 (1976), 251-278. Zbl0316.47042
18. [18] Petryshyn, W. V., On projectional solvability and the Fredholm alternative for equations involving linear A-proper operators, Arch. Rational Mech. Anal. 30 (1968), 270-284. Zbl0176.45902
19. [19] Petryshyn, W. V., Invariance of domain for locally A-proper mappings and its implications, J. Funct. Anal. 5 (1970), 137-159. Zbl0197.40501
20. [20] Petryshyn, W. V., Stability theory for linear A-proper mappings, Proc. Math. Phys. Sect. Shevchenko Sci. Soc., 1973. 
21. [21] Petryshyn, W. V., On the approximation solvability of equations involving A-proper and pseudo A-proper mappings, Bull. Amer. Math. Soc. 81 (1975), 223-448. Zbl0303.47038
22. [22] Stuart, C. A. and Toland, J. F., A global result applicable to nonlinear Steklov problems, J. Differential Equations 15 (1974), 247-268. Zbl0276.35037
23. [23] Taylor, A. E. and Lay, D. C., Introduction to Functional Analysis, 2nd ed., Wiley, New York, 1980. Zbl0501.46003
24. [24] Toland, J. F., Topological methods for nonlinear eigenvalue problems, Battelle Math. Report No. 77, 1973. 
25. [25] Toland, J. F., Global bifurcation theory via Galerkin's method, Nonlinear Anal. 1 (1977), 305-317. Zbl0477.47036
26. [26] Welsh, S. C., Global results concerning bifurcation for Fredholm maps of index zero with a transversality condition, Nonlinear Anal. 12 (1988), 1137-1148. Zbl0672.47051
27. [27] Welsh, S. C., A vector parameter global bifurcation result, ibid. 25 (1995), 1425-1435. Zbl0901.47041
28. [28] Westreich, D., Bifurcation at eigenvalues of odd multiplicity, Proc. Amer. Math. Soc. 41 (1973), 609-614. Zbl0272.58004