Existence of Solutions for Implicit Obstacle Problems of Fractional Laplacian Type Involving Set-Valued Operators

Dumitru Motreanu (), Nguyen Van Thien () and Shengda Zeng ()
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Dumitru Motreanu: Yulin Normal University
Nguyen Van Thien: FPT University
Shengda Zeng: Yulin Normal University

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 2, No 5, 407 pages

Abstract: Abstract The paper is devoted to a new kind of implicit obstacle problem given by a fractional Laplacian-type operator and a set-valued term, which is described by a generalized gradient. An existence theorem for the considered implicit obstacle problem is established, using a surjectivity theorem for set-valued mappings, Kluge’s fixed point principle and nonsmooth analysis.

Keywords: Implicit obstacle problem; Surjectivity theorem; Generalized fractional Laplacian; Generalized gradient; Fixed point theorem; 35R11; 35J50; 35J60; 26E25; 47J22 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-020-01752-4

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