Existence and multiplicity of solutions for some Styklov problem involving p(x)-Laplacian operator. Issue 7 (3rd May 2022)

• Record Type: Journal Article
• Authors: Chammem, R.; Ghanmi, A.; Sahbani, A.
• Is Part Of: Applicable analysis. Volume 101:Issue 7(2022)
• Page Start: 2401
• Page End: 2417
• Publication Date: 2022-05-03
• Subjects: M. A. Ragusa; p(x)-Laplacian -- variational methods -- variable exponents -- Ekeland principle -- generalized Sobolev space; 31B30 -- 35J35; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1807014
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we consider a class of p ( x ) -Laplacian problems of the form: 1 ( − Δ ) p ( x ) u + a ( x ) | u | p ( x ) − 2 u = f ( x, u ) in Ω, | ∇ u | p ( x ) − 2 ∂ u ∂ v + b ( x ) | u | q ( x ) − 2 u = g ( x, u ) on ∂ Ω, where Ω ⊂ R N, N ≥ 2 is a bounded domain with Lipschitz boundary ∂ Ω, ( ∂ / ∂ v ) is outer unit normal derivative. The functions a, b, p, q, g and f are assumed to satisfy suitable assymptions. The existence and the multiplicity of solutions is obtained by using variational methods, and mountain pass lemma combined with Ekeland variational principle.