5 papers
A scalar field equation on hyperbolic space with indefinite sign nonlinearity
Debabrata Karmakar, Atanu Manna, Bhakti Bhusan Manna
In this article, we study threshold phenomena for the semilinear double-power elliptic equation $$-Î_{\mathbb{B}^N} u - λu = |u|^{p-1}u - |u|^{q-1}u, \quad u \in H^1(\mathbb{B}^N…
Quantitative stability for the conformally invariant Chang-Gui inequality on the exponentiation of functions on the sphere
Monideep Ghosh, Debabrata Karmakar
In this work, we focus on a recent variant of the Trudinger-Moser-Onofri inequality introduced by S. Y. Alice Chang and Changfeng Gui \cite{CG-2023}: \begin{align*} α\int_{\mathbb…
Existence of Bianchi-Egnell stability extremizer for the Hardy-Sobolev inequality
Souptik Chakraborty, Monideep Ghosh, Debabrata Karmakar
In this article, we prove the best Bianchi-Egnell constant for the Hardy-Sobolev (HS) inequality \begin{align*} C_{\tiny\mbox{BE}}(γ) := \inf_{u \ \small \mbox{not an optimizer}}…
Total masses of solutions to general Toda systems with singular sources
Debabrata Karmakar, Chang-Shou Lin, Zhaohu Nie +1
In this article we obtain total masses of solutions to the Toda system associated to a general simple Lie algebra with singular sources at the origin. The determination of such tot…
A note on the log-perturbed Brézis-Nirenberg problem on the hyperbolic space
Monideep Ghosh, Anumol Joseph, Debabrata Karmakar
We consider the log-perturbed Brézis-Nirenberg problem on the hyperbolic space \begin{align*} Î_{\mathbb{B}^N}u+λu +|u|^{p-1}u+θu \ln u^2 =0, \ \ \ \ u \in H^1(\mathbb{B}^N), \…