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Welsh, Stewart

Contact Information
Stewart C. Welsh, Ph.D.

Office: MCS 483
Phone: 512-245-3426
Research Interests
Bifurcation Theory
Differential Equations

Professor Welsh received his Ph.D. from University of Glasgow, Scotland in 1985. Currently, Dr. Welsh has been studying sufficient conditions to ensure that the equation F(x, z) = 0, where F: X * R^n --> Y (X, Y are Banach spaces), possesses bifurcation points. More specifically, if F(0, z) = 0, for all z in R^n, then what conditions need to be imposed upon F and the underlying spaces X and Y, in order to guarantee that a branch of nontrivial solutions (F(x,z) = 0, x not zero, Z in R^n) emanates continuously from the so-called trivial solution (0, z0), where z in R^n?

Selected Publications:

  • S. C. Welsh. A generalized-degree homotopy yielding global bifurcation results. Nonlinear Anal. 62 (2005), no. 1, 89--100.
  • S. C. Welsh. One-parameter global bifurcation in a multiparameter problem. Colloq. Math., 77(1):85--96, 1998.
  • S. C. Welsh. A remark on real parameter global bifurcation. Acta Math. Hungar., 78(3):199--211, 1998.
  • S. C. Welsh. Open mappings and solvability of nonlinear equations in Banach space. Proc. Roy. Soc. Edinburgh Sect. A, 126(2):239--246, 1996.
  • S. C. Welsh. A vector parameter global bifurcation result. Nonlinear Anal., 25(12):1425--1435, 1995.
  • S. C. Welsh. A priori bounds and nodal properties for periodic solutions to a class of ordinary differential equations. J. Math. Anal. Appl., 171(2):395--406, 1992.
  • S. C. Welsh. Sufficient conditions for periodic solutions to a class of second-order differential equations. Nonlinear Anal., 17(1):85--93, 1991.
  • J. R. L. Webb and S. C. Welsh. Existence and uniqueness of initial value problems for a class of second-order differential equations. J. Differential Equations, 82(2):314--321, 1989.
  • S. C. Welsh. Global results concerning bifurcation for Fredholm maps of index zero with a transversality condition. Nonlinear Anal., 12(11):1137--1148, 1988.
  • S. C. Welsh. Bifurcation of A-proper mappings without transversality considerations. Proc. Roy. Soc. Edinburgh Sect. A, 107(1-2):65--74, 1987.
  • J. R. L. Webb and S. C. Welsh. Topological degree and global bifurcation. In Nonlinear functional analysis and its applications, Part 2 (Berkeley, Calif., 1983), pages 527--531. Amer. Math. Soc., Providence, R.I., 1986.
  • J. R. L. Webb and S. C. Welsh. A-proper maps and bifurcation theory. In Ordinary and partial differential equations (Dundee, 1984), pages 342--349. Springer, Berlin, 1985.