本文运用锥理论计算一类全连续场的拓扑度,极大地减弱了非线性算子下方 有界的条件, 因而本质上改进和推广了现有结果. 最后,把抽象结果应用于研究超线 性Hammerstein积分方程非平凡解的存在性.

In this paper, we compute, by using cone theory, the topological degree of a class of completely continuous fields where the condition on the lower boundedness of nonlinear operators is sharply weakened. Therefore our results substantially improve and generalize the existing ones in the literature. Finally we use our abstract results to establish the existence of nontrivial solutions for superlinear Hammerstein integral equations.