activity
20162026
most citedMultiplicity results for fractional elliptic equations involving critical nonlinearities

21 citations · 48 across the 18 of their papers we have counts for

collaborators

19 papers

math.AP2026

A fractional Brezis-Nirenberg problem with multipolar Hardy potentials

Debangana Mukherjee

We study a fractional Brezis--Nirenberg problem on a bounded domain with finitely many Hardy potentials centered at distinct points , with masses $μ_1,\dots,μ_k\geq…

math.AP2026

Critical fractional -Hardy Sobolev equations: Global compactness and multiplicity of positive solutions

Nirjan Biswas, Souptik Chakraborty, Debangana Mukherjee

We study the critical fractional -Hardy-Sobolev equation \begin{equation}\tag{}\label{a-main} (-Δ_p)^s u -μ\dfrac{|u|^{p-2}u}{|x|^{sp}}=\dfrac{|u|^{p^*_s(α)-2}u}{|x…

math.AP2026

Nonlocal Tikhonov Regularization: Hilbert Scales, Explicit Rates, and the Classical Limit

Debangana Mukherjee, Akash Ashirbad Panda

We study fractional-Sobolev Tikhonov regularization for linear inverse problems on a bounded Lipschitz domain. The regularization penalty is generated by the restricted Dirichlet f…

math.AP2026

Equivalence of weak and viscosity solutions for nonlocal p-Laplace type equations on the Heisenberg group

Debangana Mukherjee, Vivek Tewary

We establish the equivalence between weak and viscosity solutions for a broad class of nonlocal -Laplace type equations on the Heisenberg group whose kernels satisfy standard sy…

math.AP2026

On fractional critical problems with multi-polar Hardy potentials

Edoardo Mainini, Debangana Mukherjee, Roberto Ognibene

We investigate the existence of positive solutions to fractional equations presenting a double criticality: a multi-polar Hardy-type potential and a Sobolev critical nonlinearity.…

math.AP2021

Non-homogeneous -fractional Laplacian systems with lack of compactness

Debangana Mukherjee, Tuhina Mukherjee

The present paper studies the existence of weak solutions for the following type of non-homogeneous system of equations \begin{equation*} (S) \left\{\begin{aligned} (-Δ)^{s_1}_{p_1…

math.AP2020

On the study of semilinear non-local elliptic systems

Debangana Mukherjee, Debopriya Mukherjee

The purpose of this paper is to study the existence of solutions for semilinear elliptic system driven by fractional Laplacian and establish some new existence results which are ob…

math.AP2020★ 1 cited

On the existence of three non-negative solutions for a -Laplacian system

Debangana Mukherjee, Tuhina Mukherjee

The present paper studies the existence of weak solutions for \begin{equation*} (\mathcal{P}) \left\{\begin{aligned} (-Δ)^{s_1}_{p_1} u &=\la f_1\,(x,u,v) +g_1(x,u) \,\mbox{ in }\,…

math.AP2020

Multiplicity results for non-local elliptic problems with jumping nonlinearity

Debangana Mukherjee

The present paper studies the fractional -Laplacian boundary value problems with jumping nonlinearities at zero or infinity and obtain the existence of multiple solutions and si…

math.AP2020

On the existence of multiple solutions for fractional Brezis Nirenberg type equations

Debangana Mukherjee

The present paper studies the non-local fractional analogue of the famous paper of Brezis and Nirenberg in [4]. Namely, we focus on the following model, $$\begin{align*}\left(\math…

math.AP2020

Uniqueness of the critical point for semi-stable solution in

Fabio De Regibus, Massimo Grossi, Debangana Mukherjee

In this paper we show the uniqueness of the critical point for \emph{semi-stable} solutions of the problem $$\begin{cases} -Δu=f(u)&\text{in }Ω\\ u>0&\text{in }Ω\\ u=0&\text{on } \…

math.AP2019

A Carleman estimate for the fractional heat equation and its application in final state observability

Erika Hausenblas, Debangana Mukherjee

In the paper, we show a global Carleman estimate for the non-local heat equation. To be more precise, let $Ω\subset\RR^d$ be a bounded domain and $\CO\subsetΩ$ an open subdomain, $…

math.AP2019

On fractional multi-singular Schrödinger operators: positivity and localization of binding

Veronica Felli, Debangana Mukherjee, Roberto Ognibene

In this work we investigate positivity properties of nonlocal Schrödinger type operators, driven by the fractional Laplacian, with multipolar, critical, and locally homogeneous pot…

math.AP2018★ 6 cited

Nonlocal scalar field equations: qualitative properties, asymptotic profiles and local uniqueness of solutions

Mousomi Bhakta, Debangana Mukherjee

We study the nonlocal scalar field equation with a vanishing parameter \[ \left\{\begin{array}{lll} (-Δ)^s u+εu &=|u|^{p-2}u -|u|^{q-2}u \quad\text{in}\quad\mathbb{R}^N \\ u >0, &…

math.AP2018★ 21 cited

Multiplicity results for fractional elliptic equations involving critical nonlinearities

Mousomi Bhakta, Debangana Mukherjee

In this paper we prove the existence of infinitely many nontrivial solutions for the class of fractional elliptic equations involving concave-critical nonlinearities in…

math.AP2017★ 3 cited

Sign changing solutions of p-fractional equations with concave-convex nonlinearities

Mousomi Bhakta, Debangana Mukherjee

In this article we study the existence of sign changing solution of the following p-fractional problem with concave-critical nonlinearities: \begin{eqnarray*} (-Δ)^s_pu &=& μ|u|^{q…

math.AP2016★ 11 cited

Profile of solutions for nonlocal equations with critical and supercritical nonlinearities

Mousomi Bhakta, Debangana Mukherjee, Sanjiban Santra

We study the fractional laplacian problem (-Δ)^s u &=& u^p -εu^q \quad\text{in }\quad Ω, u &\in& H^s(Ω)\cap L^{q+1}(Ω),u &>&0 \quad\text{in }\quad Ω, u&=&0 \quad\text{in}\quad \mat…

math.AP2016

Semilinear nonlocal elliptic equations with critical and supercritical exponents

Mousomi Bhakta, Debangana Mukherjee

We study the problem \begin{eqnarray*} (-Δ)^s u &=& u^p - u^q \quad\text{in }\quad \mathbb{R}^N, u &\in& \dot{H}^s(\mathbb{R}^N)\cap L^{q+1}(\mathbb{R}^N), u&>0& \quad\text{in}\qua…

math.AP2016★ 6 cited

Multiplicity results and sign changing solutions of non-local equations with concave-convex nonlinearities

Mousomi Bhakta, Debangana Mukherjee

In this paper we prove the existence of infinitely many nontrivial solutions of the following equations driven by a nonlocal integro-differential operator with concave-convex…