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math.AP2024
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|^{…
math.AP2024
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\,…