P_1—紧映象的Altman定理的一个推广

Generalizations over the Altman Theorem for p_1-compact Mapping

该文首先利用拓扑度理论推广了关于Ｐ１－紧映象的一个不动点定理，从而推广了全连续算子情形的Ａｌｔｍａｎ定理。

In this paper,using theory of topological degree some generalizations over the Altman theorem are obtained. We set up the main theorem (i.e.Theorem 1),thus the condition of p1-compact mapping F‖Fx-x‖a≥‖Fx‖a-‖x‖a,x ∈Ωis improved from α=2 to α>1. In the end,we give a sufficient condition under which there exists a positive eigenvalue of the completely continuous operator.