Variable order nonlocal Choquard problem with variable exponents
Variable order nonlocal Choquard problem with variable exponents
In this article, we study the existence/multiplicity results for the variable order nonlocal Choquard problem with variable exponents (−Δ)p(⋅)s(⋅)u(x)=λ|u(x)|α(x)−2u(x)+∫ΩF(y,u(y))|x−y|μ(x,y)dyf(x,u(x)),x∈Ω,u(x)=0,x∈Ωc:=RN∖Ω, where Ω⊂RN is a smooth and bounded domain, N≥2, p,s,μ and α are continuous functions on RN×RN and f(x,t) is a Carathéodory function with F(x,t):=∫0tf(x,s)ds. Under suitable assumption on s,p,μ,α and …