Department of Mathematics

Blackburg, VA 24061, USA

e-mail: gao@.math.vt.edu

This paper presents a dual transformation method for obtaining the general analytic solution of one dimensional fully nonlinear equilibrium equations in phase transitions and nonlinear bifurcation analysis. By using the general duality theory proposed recently in nonconvex variational problems, a trinity extremum theorem is discovered, which reveals the intrinsic properties of this general solution.