On solvability of general nonlinear variational-like inequalities in reflexive Banach spaces

Recently, variational inequality theory has been extended and applied in various directions, see [6, 7, 8, 9, 10] and the references therein. In particular, Ding [1, 2, 3], and Ding and Tan [4] studied the existence of solutions for several nonlinear variational-like inequalities in reflexive Banach spaces. In this paper, a new class of general nonlinear variational-like inequalities in reflexive Banach spaces are introduced. Utilizing a minimax inequality due to Ding and Tan [4], we provide some efficient conditions, which ensure the existence and uniqueness of solutions for the general nonlinear variational-like inequality. Our results improve and generalize many known results in the literature.