On a Class of Weighted p-Laplace Equation with Singular Nonlinearity

Prashanta Garain*, Tuhina Mukherjee

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


This article deals with the existence of the following quasilinear degenerate singular elliptic equation: (Pλ){-div(w(x)|∇u|p-2∇u)=gλ(u),u>0inΩ,u=0on∂Ω,where Ω ⊂ Rn is a smooth bounded domain, n≥ 3 , λ> 0 , p> 1 , and w is a Muckenhoupt weight. Using variational techniques, for gλ(u) = λf(u) u-q and certain assumptions on f, we show existence of a solution to (Pλ) for each λ> 0. Moreover, when gλ(u) = λu-q+ ur, we establish existence of at least two solutions to (Pλ) in a suitable range of the parameter λ. Here, we assume q∈ (0 , 1) and r∈(p-1,ps∗-1).

Original languageEnglish
Article number110
Number of pages18
Issue number4
Publication statusPublished - 1 Aug 2020
MoE publication typeA1 Journal article-refereed


  • Multiple weak solutions
  • Singular nonlinearity
  • Variational method
  • Weighted p-Laplacian

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