Existence of Solutions for the p(x)-Laplacian Problem with Singular Term. (14th March 2010)

• Record Type: Journal Article
• Authors: Yongqiang Yongqiang, Fu Fu; Mei Mei, Yu Yu
• Other Names: Manásevich Manásevich Raul F. Raul F. Academic Editor.
• Is Part Of: Boundary value problems. Volume 2010(2010)
• Publication Date: 2010-03-14
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2010/584843
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : We study the following p ( x ) -Laplacian problem with singular term: - div ( | ∇ u | p ( x ) - 2 ∇ u ) + | u | p ( x ) - 2 u = λ | u | α ( x ) - 2 u + f ( x, u ), x ∈ Ω, u = 0, x ∈ ∂ Ω, where Ω ⊂ ℝ N is a bounded domain, 1 < p - ≤ p ( x ) ≤ p + < N . We obtain the existence of solutions in W 0 1, p ( x ) ( Ω ) .