ON PROBLEMS CONCERNING THE EQUATION FOR AWEAKLY SEMIDIFFERENTIABLE MAPPING
关于弱半可微映象方程的几个问题

In this paper, the weakly semidifferentiability, the weakly semiderivative ofmappings and the fixed point index for a class of 1-set contractions are introduced,and applied to the study of problem regarding positive solutions, the multiple positive solutions to the equation concerned, and the positive eigenvalues and eigenvectors.Also, improvements and developments of some results by Petryshyn, Legget andWilliams, Amann, Edmunds and others are presented in the paper.