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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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2018/6953649 |
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| author | Teffera M. Asfaw |
| author_facet | Teffera M. Asfaw |
| author_sort | Teffera M. Asfaw |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-332f033eca04414cae54e4d34478d689 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-332f033eca04414cae54e4d34478d6892025-08-20T02:24:21ZengWileyAbstract and Applied Analysis1085-33751687-04092018-01-01201810.1155/2018/69536496953649Existence Theorems on Solvability of Constrained Inclusion Problems and ApplicationsTeffera M. Asfaw0Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USALet 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.http://dx.doi.org/10.1155/2018/6953649 |
| spellingShingle | Teffera M. Asfaw Existence Theorems on Solvability of Constrained Inclusion Problems and Applications Abstract and Applied Analysis |
| title | Existence Theorems on Solvability of Constrained Inclusion Problems and Applications |
| title_full | Existence Theorems on Solvability of Constrained Inclusion Problems and Applications |
| title_fullStr | Existence Theorems on Solvability of Constrained Inclusion Problems and Applications |
| title_full_unstemmed | Existence Theorems on Solvability of Constrained Inclusion Problems and Applications |
| title_short | Existence Theorems on Solvability of Constrained Inclusion Problems and Applications |
| title_sort | existence theorems on solvability of constrained inclusion problems and applications |
| url | http://dx.doi.org/10.1155/2018/6953649 |
| work_keys_str_mv | AT tefferamasfaw existencetheoremsonsolvabilityofconstrainedinclusionproblemsandapplications |