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• W3178665633 abstract "The purpose of the present paper is to study the existence of solutions for the following nonhomogeneous singular problem involving the fractional p(x,.)-Laplace operator {(−Δ)p(x,.)su+|u|q(x)−2u=g(x)uϵ−1−γ(x)∓λf(x,u)in Ω,u=0on ∂Ω,where Ω is a smooth bounded domain in RN (N≥3), 0<s,ϵ<1, λ is a positive parameter and γ:Ω¯⟶(0,ϵ) is a continuous function, p:Ω¯×Ω¯⟶(1,∞) is a bounded, continuous and symmetric function, q:Ω¯⟶(1,∞) is a continuous function, g∈Lps∗(x)−ϵps∗(x)+γ(x)−2ϵ(Ω) and g(x)>0 with ps∗(x)=Np(x,x)N−sp(x,x). Here, the nonlinearity f is in C1(Ω¯×R) and assumed to satisfy suitable assumptions. Using variational methods combined with monotonicity arguments, we obtain the existence of solutions to the problem in a fractional Sobolev space with variable exponent. To our best knowledge, this paper is the first attempt in the study of singular problems involving fractional p(x,.)-Laplace operators." @default.
• W3178665633 created "2021-07-19" @default.
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• W3178665633 date "2021-07-05" @default.
• W3178665633 modified "2023-09-24" @default.
• W3178665633 title "On some singular problems involving the fractional <i>p</i>(<i>x</i>,.) -Laplace operator" @default.
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• W3178665633 doi "https://doi.org/10.1080/00036811.2021.1950693" @default.
• W3178665633 hasPublicationYear "2021" @default.
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