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Existence of solutions for an anisotropic elliptic problem with variable exponent and singularity
Author(s) -
Yu Mei,
Wang Li,
Tang Sufang
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3729
Subject(s) - mathematics , singularity , bounded function , exponent , domain (mathematical analysis) , anisotropy , mathematical analysis , critical exponent , variable (mathematics) , boundary (topology) , elliptic curve , critical point (mathematics) , point (geometry) , geometry , physics , philosophy , linguistics , quantum mechanics , scaling
In this paper, we study the following anisotropic problem with singularity:− ∑ i = 1 N∂x i| ∂x iu |p i ( x ) − 2∂x iu = λ | u | q ( x ) − 2 u | x | s ( x )+ f ( x , u ) , x ∈ Ω ,u = 0 , x ∈ ∂ Ω ,where Ω ⊂ R Nis 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.