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math.AP2025
Existence of a bi-radial sign-changing solution for Hardy-Sobolev-Mazya type equation
Atanu Manna, Bhakti Bhusan Manna
In this article, we study the following Hardy-Sobolev-Maz'ya type equation: \begin{equation} -Δu - μ\frac{u}{|z|^2} = \frac{|u|^{q-2}u}{|z|^t}, \quad u \in D^{1,2} (\mathbb{R}^n),…
math.AP2025
Spike layered solutions for elliptic systems on Riemannian Manifolds
Anusree R Kannoth, Bhakti Bhusan Manna
In this article, we study the following Hamiltonian system: \begin{equation*} \begin{cases} \begin{aligned} &-\varepsilon^{2}Δ_{g} u +u = |v|^{q-1}v, &-\varepsilon^{2}Δ_{g} v +v =…