50205
博碩士論文
Mathematics
A basic problem is that of finding nontrivial solutions of the following nonlinear eigenvalue problem: $-\Delta$u = $\lambda$F$\prime$ (u) in D, u = 0 on $\partial$D, where D is a domain in R$\sp{\rm N}$, N = 1,2,3, and F$\prime$(u) is non-monotone. Problems of this kind arise, for example, in plasma physics, fluid dynamics, and astrophysics. In the first part of this thesis, an equivalent variational formulation is used to obtain an iterative procedure for solving the problem with a general fun...