Existence of Solutions for Degenerate Elliptic Problems in Weighted Sobolev Space. (2nd December 2015)

• Record Type: Journal Article
• Authors: Dai, Lili; Gao, Wenjie; Li, Zhongqing
• Other Names: Phuc Nguyen C. Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-12-02
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/265127
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This paper is devoted to the study of the existence of solutions to a general elliptic problemA u + g ( x, u, ∇ u ) = f - div ⁡ F, withf ∈ L 1 ( Ω ) andF ∈ ∏ i = 1 N L p ' ( Ω, ω i * ), whereA is a Leray-Lions operator from a weighted Sobolev space into its dual andg ( x, s, ξ ) is a nonlinear term satisfyingg x, s, ξ sgn ⁡ ( s ) ≥ ρ ∑ i = 1 N ω i | ξ i | p, | s | ≥ h > 0, and a growth condition with respect toξ . Here, ω i, ω i * are weight functions that will be defined in the Preliminaries.