Existence of solutions for an anisotropic elliptic problem with variable exponent and singularity. (14th October 2015)

• Record Type: Journal Article
• Authors: Yu, Mei; Wang, Li; Tang, Sufang
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 10(2016:Jul. 15)
• Page Start: 2761
• Page End: 2767
• Publication Date: 2015-10-14
• Subjects: anisotropic Sobolev spaces -- singularity -- critical point theory; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3729
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we study the following anisotropic problem with singularity: − ∑ i = 1 N ∂ x i | ∂ x i u | p i ( x ) − 2 ∂ x i u = λ | u | q ( x ) − 2 u | x | s ( x ) + f ( x, u ), x ∈ Ω, u = 0, x ∈ ∂ Ω, where Ω ⊂ R N is a bounded domain with smooth boundary. Using the critical point theory, we obtain the existence of weak solutions for the problem under suitable conditions. Copyright © 2015 John Wiley & Sons, Ltd.