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Title

One-parameter global bifurcation in a multiparameter problem

Authors 1

Affiliations

  1. Department of Mathematics, Southwest Texas, State University, San Marcos, Texas 78666

Bibliography

  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.
  2. Alexander, J. C. and Fitzpatrick, P. M., Galerkin approximations in several parameter bifurcation problems, Math. Proc. Cambridge Philos. Soc. 87 (1980), 489-500.
  3. Alexander, J. C. and Yorke, J. A., Global bifurcation of periodic orbits, Amer. J. Math. 100 (1978), 263-292.
  4. Cantrell, R. S., A homogeneity condition guaranteeing bifurcation in multiparameter nonlinear eigenvalue problems, Nonlinear Anal. 8 (1984), 159-169.
  5. Cantrell, Multiparameter bifurcation problems and topological degree, J. Differential Equations 52 (1984), 39-51.
  6. Crandall, M. G. and Rabinowitz, P. H., Bifurcation from simple eigenvalues, J. Funct. Anal. 8 (1971), 321-340.
  7. Esquinas, J. and López-Gómez, J., Optimal multiplicity in local bifurcation theory. I. Generalized generic eigenvalues, J. Differential Equations 71 (1988), 71-92.
  8. Esquinas, J. and López-Gómez, J., Optimal multiplicity in bifurcation theory. II. General case, ibid. 75 (1988), 206-215.
  9. Esquinas, J. and López-Gómez, J., Multiparameter bifurcation for some reaction-diffusion systems, Proc. Roy. Soc. Edinburgh Sect. A 112 (1989), 135-143.
  10. Fitzpatrick, P. M., Homotopy, linearization and bifurcation, Nonlinear Anal. 12 (1988), 171-184.
  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.
  12. Hale, J. K., Bifurcation from simple eigenvalues for several parameter families, Nonlinear Anal. 2 (1978), 491-497.
  13. Ize, J., Bifurcation theory for Fredholm operators, Mem. Amer. Math. Soc. 174 (1976).
  14. Ize, J., Necessary and sufficient conditions for multiparameter bifurcation, Rocky Mountain J. Math. 18 (1988), 305-337.
  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.
  16. López-Gómez, J., Multiparameter bifurcation based on the linear part, J. Math. Anal. Appl. 138 (1989), 358-370.
  17. Magnus, R. J., A generalization of multiplicity and the problem of bifurcation, Proc. London Math. Soc. 32 (1976), 251-278.
  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.
  19. Petryshyn, W. V., Invariance of domain for locally A-proper mappings and its implications, J. Funct. Anal. 5 (1970), 137-159.
  20. Petryshyn, W. V., Stability theory for linear A-proper mappings, Proc. Math. Phys. Sect. Shevchenko Sci. Soc., 1973.
  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.
  22. Stuart, C. A. and Toland, J. F., A global result applicable to nonlinear Steklov problems, J. Differential Equations 15 (1974), 247-268.
  23. Taylor, A. E. and Lay, D. C., Introduction to Functional Analysis, 2nd ed., Wiley, New York, 1980.
  24. Toland, J. F., Topological methods for nonlinear eigenvalue problems, Battelle Math. Report No. 77, 1973.
  25. Toland, J. F., Global bifurcation theory via Galerkin's method, Nonlinear Anal. 1 (1977), 305-317.
  26. Welsh, S. C., Global results concerning bifurcation for Fredholm maps of index zero with a transversality condition, Nonlinear Anal. 12 (1988), 1137-1148.
  27. Welsh, S. C., A vector parameter global bifurcation result, ibid. 25 (1995), 1425-1435.
  28. Westreich, D., Bifurcation at eigenvalues of odd multiplicity, Proc. Amer. Math. Soc. 41 (1973), 609-614.
Colloquium Mathematicum
1998/77/1
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Pages:
85-96
Main language of publication
English
Received
1997-06-04
Accepted
1997-11-05
Published
1998
Exact and natural sciences