Abstract: The strong dependence of fusion reaction rate on ion temperature leads to a thermalinstability of D T burning plasma.Mathematical qualites are discussed for the non-linear differential equations describing the steady state power balance of a D T burning plasma.Shooting method is used to obtain equilibrium solution and eigenvalue of the linearized equation about temperature pertubation around equilibrium.How ever,the solution obtained by the above method can be different from the time-dependent one for t→∞.This provides a typical example of a kind of unsolved non-linear mathematical problem.

Key words: Nonlinear differential equation, Shooting method, Inconsistency between solutions