E-resources
PDF-
Garain, Prashanta; Mukherjee, Tuhina
Mediterranean journal of mathematics, 08/2020, Volume: 17, Issue: 4Journal Article
This article deals with the existence of the following quasilinear degenerate singular elliptic equation: ( P λ ) - div ( w ( x ) | ∇ u | p - 2 ∇ u ) = g λ ( u ) , u > 0 in Ω , u = 0 on ∂ Ω , where Ω ⊂ R n is a smooth bounded domain, n ≥ 3 , λ > 0 , p > 1 , and w is a Muckenhoupt weight. Using variational techniques, for g λ ( u ) = λ f ( u ) u - q and certain assumptions on f , we show existence of a solution to ( P λ ) for each λ > 0 . Moreover, when g λ ( u ) = λ u - q + u r , we establish existence of at least two solutions to ( P λ ) in a suitable range of the parameter λ . Here, we assume q ∈ ( 0 , 1 ) and r ∈ ( p - 1 , p s ∗ - 1 ) .
