Existence Theorems on Solvability of Constrained Inclusion Problems and Applications

Teffera M. Asfaw

Abstract and Applied Analysis, 2018, vol. 2018, issue 1

Abstract: 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.

Date: 2018
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https://doi.org/10.1155/2018/6953649

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2018:y:2018:i:1:n:6953649

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