Asfaw, Teffera M.Asfaw, Teffera M.2018-07-162018-07-162018-07-12Teffera M. Asfaw, “Existence Theorems on Solvability of Constrained Inclusion Problems and Applications,” Abstract and Applied Analysis, vol. 2018, Article ID 6953649, 10 pages, 2018. doi:10.1155/2018/6953649http://hdl.handle.net/10919/83966Let 𝑋 be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space 𝑋∗. Let𝑇 : 𝑋 ⊇ 𝐷(𝑇) → 2𝑋∗ be a maximal monotone operator and 𝐶 : 𝑋 ⊇ 𝐷(𝐶) → 𝑋∗ be bounded and continuous with 𝐷(𝑇) ⊆ 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 underweak 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.application/pdfenCreative Commons Attribution 4.0 InternationalArticle - Refereed2018-07-15Copyright © 2018 Teffera M. Asfaw. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.https://doi.org/10.1155/2018/6953649