Existence of solutions for non-coercive variational-hemivariational inequalities involving the nonlocal fractional p-Laplacian. (4th March 2022)

• Record Type: Journal Article
• Authors: Liu, Yongjian; Liu, Zhenhai; Wen, Ching-Feng; Yao, Jen-Chih
• Is Part Of: Optimization. Volume 71:Number 3(2022)
• Page Start: 485
• Page End: 503
• Publication Date: 2022-03-04
• Subjects: Hemivariational inequalities -- nonlocal fractional p-Laplacian -- non-coercivity -- existence of solutions; 35R11 -- 49J52; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1808643
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we study the existence of solutions for non-coercive variational-hemivariational inequalities involving nonlocal fractional p-Laplacian. Our approach is based on the theory of pseudomonotone operators in the sense of Brézis, recession analysis and the properties of nonlocal fractional p-Laplace operators recently established.The innovation of this paper is that we do not assume the usual coercivity or smallness assumptions as stated in most existing literature. The absence of such assumptions will make the existence of solutions very complicated. We have to proceed from the specific problem itself and seek specific methods based on the inherent characteristics of different problems.