Characterizations for solidness of dual cones with applications

In this paper, some characterizations for the solidness of dual cones are established. As applications, we prove that a Banach space is reflexive if it contains a solid pointed closed convex cone having a weakly compact base, and prove an analogue of a Karamardian’s result for the linear complementarity problem in reflexive Banach spaces. The uniqueness of the solution of the linear complementarity problem is also discussed.