The paper deals with one important class of reaction-diffusion equations, u' + μ(u - uk) = 0(2 ≤ k ∈ Z+) with boundary value condition u(0) = u(π) = 0. Singularity theory based on the method of L-S (Liapunov-Schmidt) is applied to its bifurcation analysis. And the satisfactory results are obtained.
The explicit expression for the generalized inverse AT,S2 in [6]is utilized in presenting the minors of the generalized inverse AT,S2. Thus, without calculating M-P inverse, weighted M-P inverse, group inverse and Drazin inverse, we are able to find the minors of them. The main results are also the generalization of the results proposed by [5] and [8].
A new proof of the row Cayley-Hamilton theorem for 2-D system was given in this note. In a similar way, the Column Cay- ley-Hamilton theorem was also presented and proved.
