Existence theorems on solvability of constrained inclusion problems and applications (Q1728533)

Summary: Let \(X\) be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space \(X^\ast\). Let \(T : X \supseteq D(T) \rightarrow 2^{X^\ast}\) be a maximal monotone operator and \(C : X \supseteq D(C) \rightarrow X^\ast\) be bounded and continuous with \(D(T) \subseteq D(C)\). The paper provides new existence theorems concerning solvability of inclusion problems involving operators of the type \(T + C\) provided that \(C\) is compact or \(T\) 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 \(T + C\). The operator \(C\) 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.