一类弱连续映射的拓扑度及其应用

THE TOPOLOGICAL DEGREE THEORY OF SOME WEAKLY CONTINUOUS FUNCTIONS AND ITS APPLICATIONS

对一类弱连续映射建立了多值拓扑度,获得了可解性,广义可加性,同伦不变性和切除性等基本性质,并得到了奇映射定理和锐角原理.最后还利用所得结果,讨论了非线性算子方程的解的存在性问题、广义固有值问题及拟线性椭圆特征问题.改进了这些方面已有的结果.

A topological degree theory is set up for some weakly continuous functions. Some basic characteristics, i. e. the resolvability, the generalized additivity, the homotopy invariance and the excision,etc. are obtained. The odd mapping theorem and the Acute Angle principle are also obtained. Finally,with these results, we discussed the existence problem of solutions of a nonlinear operator equationand the generalized eigenvalue problem and the Dirichlet problem of a quasilinear elliptic equation.