Multiple solutions for a fractional Choquard problem with slightly subcritical exponents on bounded domains

Positive Blowup Solutions for Some Fractional Systems in Bounded Domains

Using some potential theory tools and the Schauder fixed point theorem, we prove the existence of a positive continuous weak solution for the fractional system (−∆)u+ p(x)uv = 0, (−∆)v + q(x)uv = 0 in a bounded C1,1-domain D in Rn (n ≥ 3), subject to Dirichlet conditions, where 0 < α < 2, σ, β ≥ 1, s, r ≥ 0. The potential functions p, q are nonnegative and required to satisfy some adequate hypo...

Existence of non-trivial solutions for fractional Schrödinger-Poisson systems with subcritical growth

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + u + λφu = µf(u) +|u|p−2|u|, x ∈R3 (−∆t)φ = u2, x ∈R3 where λ,µ are two parameters, s,t ∈ (0,1] ,2t + 4s > 3 ,1 < p ≤ 2∗ s and f : R → R is continuous function. Using some critical point theorems and truncation technique, we obtain the existence and multiplicity of non-trivial solutions with ...

Fractional Cauchy problems on bounded domains

Fractional Cauchy problems replace the usual first-order time derivative by a fractional derivative. This paper develops classical solutions and stochastic analogues for fractional Cauchy problems in a bounded domain D ⊂ Rd with Dirichlet boundary conditions. Stochastic solutions are constructed via an inverse stable subordinator whose scaling index corresponds to the order of the fractional ti...

Space–time fractional diffusion on bounded domains

Distributed-order fractional diffusions on bounded domains