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?

• 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.