Open Access
2018 Existence Theorems on Solvability of Constrained Inclusion Problems and Applications
Teffera M. Asfaw
Abstr. Appl. Anal. 2018: 1-10 (2018). DOI: 10.1155/2018/6953649


Let X be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space X * . Let T : X D ( T ) 2 X * 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.


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Teffera M. Asfaw. "Existence Theorems on Solvability of Constrained Inclusion Problems and Applications." Abstr. Appl. Anal. 2018 1 - 10, 2018.


Received: 10 March 2018; Accepted: 7 June 2018; Published: 2018
First available in Project Euclid: 19 September 2018

zbMATH: 07029292
MathSciNet: MR3831159
Digital Object Identifier: 10.1155/2018/6953649

Rights: Copyright © 2018 Hindawi

Vol.2018 • 2018
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