6 papers
Mixed double phase equations with local and nonlocal operators
Anupma Arora, Shilpa Gupta, Patrick Winkert
In this paper, we study a new class of mixed double phase problems that combine local and nonlocal operators. We consider two different models. The first model is driven by the fra…
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 p…
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 $$ \left\{ \begin{array}{lr} (a+b\int_{\mathbb{R}^N}|(-Î)^{\frac{s}{2}} u|^2\;dx)(-Î)^su=λ_1u+(I_μ…
Ground state solution for a generalized Choquard Schrodinger equation with vanishing potential in homogeneous fractional Musielak Sobolev spaces
Shilpa Gupta, Gaurav Dwivedi
This paper aims to establish the existence of a weak solution for the following problem: \begin{equation*} (-Î)^{s}_{\mathcal{H}}u(x) +V(x)h(x,x,|u|)u(x)=\left(\int_{\mathbb{R}^{N…
Critical -fractional problems involving a sandwich type nonlinearity
Mousomi Bhakta, Alessio Fiscella, Shilpa Gupta
In this paper, we deal with the following -fractional problem $$ (-Î)^{s_{1}}_{p}u +(-Î)^{s_{2}}_{q}u=λP(x)|u|^{k-2}u+θ|u|^{p_{s_{1}}^{*}-2}u \, \mbox{ in }\, Ω,\qquad…
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) Îu =λu+α(I_μ\ast|u|^{q})|u|^{q-2}u+(I_μ\as…