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Profile decomposition and multiple positive solutions for the perturbed CR Yamabe equation on the Heisenberg group
Riju Basak, Souptik Chakraborty, Tapendu Rana +1
In this article, we study an inhomogeneous critical nonlinear equation involving the sub-Laplacian on the Heisenberg group . We prove the multiplicity of positive solu…
On the sharp multi-bubble stability for fractional Hardy-Sobolev equations -- A quantitative approach in low dimensions
Souptik Chakraborty, Utsab Sarkar
We establish sharp quantitative multi-bubble stability for non-sign-changing critical points of the fractional Hardy-Sobolev inequality in the low-dimensional regime .…
Mixed local-nonlocal equations with critical nonlinearity on : Non-existence, Existence, and Multiplicity of positive solutions
Nirjan Biswas, Souptik Chakraborty, Paramananda Das
We consider the following quasilinear critical problem involving the mixed local-nonlocal operator: \begin{equation}\label{main_prob_abstract_1}\tag{} -Δ_p u+(-Δ_p)^…
Global Compactness Result for a Brézis-Nirenberg-Type Problem Involving Mixed Local Nonlocal Operator
Souptik Chakraborty, Diksha Gupta, Shammi Malhotra +1
This paper investigates the profile decomposition of Palais-Smale sequences associated with a Brezis-Nirenberg type problem involving a combination of mixed local nonlocal operator…
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}} \…
On -fractional weakly-coupled system with critical nonlinearities
Nirjan Biswas, Souptik Chakraborty
This paper deals with the following nonlocal system of equations: \begin{equation}\tag{}\label{MAT1} (-Δ_p)^s u = \fracα{p_s^*}|u|^{α-2}u|v|^β+f(x) \text{ in } \mathbb{…