On a p⋅-biharmonic problem of Kirchhoff type involving critical growth. Issue 16 (2nd November 2022)

• Record Type: Journal Article
• Authors: Chung, Nguyen Thanh; Ho, Ky
• Is Part Of: Applicable analysis. Volume 101:Issue 16(2022)
• Page Start: 5700
• Page End: 5726
• Publication Date: 2022-11-02
• Subjects: Variable exponent Lebesgue–Sobolev spaces -- concentration-compactness principle -- p(⋅)-biharmonic operator -- genus theory -- variational methods; 35B33 -- 35J20 -- 35J60 -- 35G30 -- 46E35 -- 49J35; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1903445
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We establish a concentration-compactness principle for the Sobolev space W 2, p ( ⋅ ) ( Ω ) ∩ W 0 1, p ( ⋅ ) ( Ω ) that is a tool for overcoming the lack of compactness of the critical Sobolev imbedding. Using this result, we obtain several existence and multiplicity results for a class of Kirchhoff type problems involving p ( ⋅ ) -biharmonic operator and critical growth.