非线性项含零点的二阶Dirichlet问题结点解集的全局结构

用Rabinowitz全局分歧定理, 研究二阶Dirichlet边值问题结点解集的全局结构, 其中r为正参数, a: ［0,1］→［0,∞)连续且允许其在［0,1］的 部分真子区间上恒为0, f: R→R在0和∞处是渐近线性的且有两个非0零点.

Global Structure of Nodal Solution Set of Second-Order Dirichlet Problems of Nonlinear Terms with Zero Points

By using the Rabinowitz global bifurcation theorem, the author studies the global structure of nodal solution set of second-order Dirichlet boundary problem, where r is a positive parameter, a: ［0,1］→［0,∞) is continuous and allowed to be constant at 0 in some proper subinterval of ［0,1］. f: R→R is continuous, asymptotically linear at 0 and ∞. There are two non-zero zero points of f.