Existence Theorems on Solvability of Constrained Inclusion Problems and Applications

Let X be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space X⁎. Let T: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 problem...

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Bibliographic Details
Main Author: Teffera M. Asfaw
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2018/6953649
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Summary:Let X be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space X⁎. Let T: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 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.
ISSN:1085-3375
1687-0409