4 papers
Normalized solution to Kirchhoff-fractional system involving critical Choquard nonlinearity
Divya Goel, Shilpa Gupta, Asmita Rai
In this article, we explore the fractional Kirchhoff-Choquard system given by $$ \left\{ \begin{array}{lr} (a+b\int_{\mathbb{R}^N}|(-Δ)^{\frac{s}{2}} u|^2\;dx)(-Δ)^su=λ_1u+(I_μ*|v|…
Fractional -Laplace systems with critical Hardy nonlinearities: Existence and Multiplicity
Nirjan Biswas, Paramananda Das, Shilpa Gupta
Let be a bounded open set containing zero, and . In this paper, we first deal with the existence, non-existence and some pr…
Normalized Solutions to the Kirchhoff-Choquard Equations with Combined Growth
Divya Goel, Shilpa Gupta
This paper is devoted to the study of the following nonlocal equation: \begin{equation*} -\left(a+b\|\nabla u\|_{2}^{2(θ-1)}\right) Δu =λu+α(I_μ\ast|u|^{q})|u|^{q-2}u+(I_μ\ast|u|^{…
Critical -fractional problems involving a sandwich type nonlinearity
Mousomi Bhakta, Alessio Fiscella, Shilpa Gupta
In this paper, we deal with the following -fractional problem $$ (-Δ)^{s_{1}}_{p}u +(-Δ)^{s_{2}}_{q}u=λP(x)|u|^{k-2}u+θ|u|^{p_{s_{1}}^{*}-2}u \, \mbox{ in }\, Ω,\qquad u=0\,…