自反Banach空间内的一般非线性变分不等式(英文)

ON GENERAL NONLINEAR VARIATIONAL INEQUALITIES IN REFLEXIVE BANACH SPACES *

在自反Ｂａｎａｃｈ空间内研究了一类一般非线性变分不等式．它包含了经典变分不等式及其各类推广作为特例．由应用极小极大不等式和辅助原理技巧，一般非线性变分不等式解的某些存在唯一性定理在自反Ｂａｎａｃｈ空间内被证明．

This paper studies a class of general nonlinear variational inequalities under reflexive Banach space setting which includes the classical variational inequalities and its various generalizations as special cases. By applying a minimax inequality and the auxiliary principle, some existence uniqueness theorems for solutions to the general nonlinear variational inequalities are proved under the setting of reflexive Banach spaces.