Topological degree theories for continuous perturbations of resolvent compact maximal monotone operators, existence theorems and applications
Volume 13, Issue 5, pp 239--257
http://dx.doi.org/10.22436/jnsa.013.05.02
Publication Date: March 03, 2020
Submission Date: September 06, 2019
Revision Date: January 10, 2020
Accteptance Date: January 16, 2020
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Authors
Teffera M. Asfaw
- Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
Abstract
Let \(X\) be a real locally uniformly convex reflexive Banach space. Let \(T: X\supseteq D(T)\to 2^{X^*}\) and \(A:X\supseteq D(A)\to 2^{X^*}\) be
maximal monotone operators such that \(T\) is of compact resolvents and \(A\) is strongly quasibounded, and \(C: X\supseteq D(C)\to X^*\) be a bounded and continuous operator with \(D(A)\subseteq D(C)\) or \(D(C)=\overline{U}\). The set \(U\) is a nonempty and open (possibly unbounded) subset of \(X\). New degree mappings are constructed for operators of the type \(T+A+C\). The operator \(C\) is neither pseudomonotone type nor defined everywhere. The theory for the case \(D(C)=\overline{U}\) presents a new degree mapping for possibly unbounded \(U\) and both of these theories are new even when \(A\) is identically zero. New existence theorems are derived. The existence theorems are applied to prove the existence of a solution for a nonlinear variational inequality problem.
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ISRP Style
Teffera M. Asfaw, Topological degree theories for continuous perturbations of resolvent compact maximal monotone operators, existence theorems and applications, Journal of Nonlinear Sciences and Applications, 13 (2020), no. 5, 239--257
AMA Style
Asfaw Teffera M., Topological degree theories for continuous perturbations of resolvent compact maximal monotone operators, existence theorems and applications. J. Nonlinear Sci. Appl. (2020); 13(5):239--257
Chicago/Turabian Style
Asfaw, Teffera M.. "Topological degree theories for continuous perturbations of resolvent compact maximal monotone operators, existence theorems and applications." Journal of Nonlinear Sciences and Applications, 13, no. 5 (2020): 239--257
Keywords
- Compact resolvents
- continuous operator
- degree theory
- variational inequality
- homotopy invariance
- maximal monotone
MSC
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