伪单调算子紧扰动的值域

Ranges of Sums for Compact Perturbations of Pseudo-monotone Operators

设 X是自反 Banach空间且 X和 X*均为局部一致凸空间 ,D是 X的开、有界、凸子集 ,T∶D→X*是伪单调算子 (pseudo-monotone) ,C∶D→ X*是紧算子或全连续算子 .利用 (S+)型算子的度理论 ,我们建立了 T+C值域性质的几个结果 .

Let X be a reflexive Banach space with both X and X * locally uniformly convex. D is a bounded, open, convex subset of X. T∶D→X * is a pseudo\|monotone operator; C∶D→X * is a compact or strongly continuous operator. By degree theory of operator of type (S\-+) , certain range properties of T+C are established. The results applied to the study of existence of some partial differential equations under various boundary conditions.