Existence Theorems on Solvability of Constrained Inclusion Problems and Applications

Let be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space . Let be a maximal monotone operator and be bounded and continuous with . The paper provides new existence theorems concerning solvability of inclusion problems involving operators of the type provided that is compact or is of compact resolvents under weak boundary condition. The Nagumo degree mapping and homotopy invariance results are employed. The paper presents existence results under the weakest coercivity condition on . The operator is neither required to be defined everywhere nor required to be pseudomonotone type. The results are applied to prove existence of solution for nonlinear variational inequality problems.