30 citations · 117 across the 36 of their papers we have counts for
40 papers
Gromov-Hausdorff Stability and Rigidity of manifolds via Heisenberg-Pauli-Weyl Uncertainty Principle
Mousomi Bhakta, Debdip Ganguly, Debabrata Karmakar
The classical Heisenberg Pauli Weyl (HPW) inequality exhibits a strong rigidity phenomenon on Riemannian manifolds i.e. on Cartan Hadamard manifolds and those with non-negative Ric…
Brezis-Nirenberg problems for mixed local-nonlocal operators with superlinear perturbations: compactness and applications
Mousomi Bhakta, Nirjan Biswas, Paramananda Das
In this paper, we consider the following mixed local nonlocal Brezis-Nirenberg problem \begin{equation}\label{crit_pro_abstract}\tag{} -Δu+(-Δ)^s u=λ|u|^{p-2}u+|…
Liouville results for supersolutions of fractional -Laplacian equations with gradient nonlinearities
Mousomi Bhakta, Anup Biswas, Aniket Sen
We prove that any nonnegative viscosity solution of the inequality must be constant. This re…
Liouville results for -Laplacian elliptic equations with source terms involving gradient nonlinearities
Mousomi Bhakta, Anup Biswas, Roberta Filippucci
In this paper, we present a series of Liouville-type theorems for a class of nonhomogeneous quasilinear elliptic equations featuring reactions that depend on the solution and its g…
Liouville properties for differential inequalities with Laplacian operator
Mousomi Bhakta, Anup Biswas, Roberta Filippucci
In this paper, we establish several Liouville-type theorems for a class of nonhomogenenous quasilinear inequalities. In the first part, we prove various Liouville results associate…
Quasilinear problems with mixed local-nonlocal operator and concave-critical nonlinearities: Multiplicity of positive solutions
Mousomi Bhakta, Nirjan Biswas, Paramananda Das
We study the existence and multiplicity of positive solutions for the following concave-critical problem driven by an operator of mixed order obtained by the sum of the classical $…
Fractional Schrödinger equations with mixed nonlinearities: asymptotic profiles, uniqueness and nondegeneracy of ground states
Mousomi Bhakta, Paramananda Das, Debdip Ganguly
We study the fractional Schrödinger equations with a vanishing parameter: where $s\in…
Poincaré-Sobolev equations with the critical exponent and a potential in the hyperbolic space
Mousomi Bhakta, Debdip Ganguly, Diksha Gupta +1
On the hyperbolic space, we study a semilinear equation with non-autonomous nonlinearity having a critical Sobolev exponent. The Poincaré-Sobolev equation on the hyperbolic space e…
Critical -fractional problems involving a sandwich type nonlinearity
Mousomi Bhakta, Alessio Fiscella, Shilpa Gupta
In this paper, we deal with the following -fractional problem $$ (-Δ)^{s_{1}}_{p}u +(-Δ)^{s_{2}}_{q}u=λP(x)|u|^{k-2}u+θ|u|^{p_{s_{1}}^{*}-2}u \, \mbox{ in }\, Ω,\qquad u=0\,…
Global compactness result and multiplicity of solutions for a class of critical exponent problem in the hyperbolic space
Mousomi Bhakta, Debdip Ganguly, Diksha Gupta +1
This paper deals with the global compactness and multiplicity of positive solutions to problems of the type $$ -Δ_{\mathbb B^N} u -λu=a(x) |u|^{2^*-2}u+f(x) \quad\text{in } \mathbb…
A system of equations involving the fractional -Laplacian and doubly critical nonlinearities
Mousomi Bhakta, Kanishka Perera, Firoj Sk
This paper deals with existence of solutions to the following fractional -Laplacian system of equations \begin{equation*} %\tag{}\label{MAT1} \begin{cases} (-Δ_p)^s…
Sharp quantitative stability of Struwe's decomposition of the Poincaré-Sobolev inequalities on the hyperbolic space: Part I
Mousomi Bhakta, Debdip Ganguly, Debabrata Karmakar +1
A classical result owing to Mancini and Sandeep [Ann. Sc. Norm. Super. Pisa Cl. Sci. 7 (2008)] asserts that all positive solutions of the Poincaré-Sobolev equation on the hyperboli…
Sharp quantitative stability of Poincare-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows
Mousomi Bhakta, Debdip Ganguly, Debabrata Karmakar +1
Consider the Poincaré-Sobolev inequality on the hyperbolic space: for every and there exists a best constant …
Fractional Hardy equations with critical and supercritical exponents
Mousomi Bhakta, Debdip Ganguly, Luigi Montoro
We study the existence/nonexistence and qualitative properties of the positive solutions to the problem \begin{align*} (-Δ)^s u -θ\frac{u}{|x|^{2s}}&=u^p - u^q \quad\text{in }\,\,…
Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data
Mousomi Bhakta, Moshe Marcus, Phuoc-Tai Nguyen
We study boundary value problems with measure data in smooth bounded domains , for semilinear equations involving Hardy type potentials. Specifically we consider problems of the…
On the bounds of the sum of eigenvalues for a Dirichlet problem involving mixed fractional Laplacians
Huyuan Chen, Mousomi Bhakta, Hichem Hajaiej
In this paper, we show the existence of a sequence of eigenvalues for a Dirichlet problem involving two mixed fractional operators with different orders. We provide lower and upper…
Fractional elliptic systems with critical nonlinearities
Mousomi Bhakta, Souptik Chakraborty, Olimpio H. Miyagaki +1
In this paper we study positive solutions to the following nonlocal system of equations: \begin{equation*} \left\{\begin{aligned} &(-Δ)^s u = \fracα{2_s^*}|u|^{α-2}u|v|^β+f(x)\;\;\…
Fractional Hardy-Sobolev equations with nonhomogeneous terms
Mousomi Bhakta, Souptik Chakraborty, Patrizia Pucci
The paper deals with existence and multiplicity of positive solutions to nonlocal equations with critical Hrardy-Sobolev nonlinearities and external terms. We establish the profile…
Nonhomogeneous systems involving critical or subcritical nonlinearities
Mousomi Bhakta, Souptik Chakraborty, Patrizia Pucci
This paper deals with existence of a nontrivial positive solution to systems of equations involving nontrivial nonhomogeneous terms and critical or subcritical nonlinearities. Via…
On multiplicity of positive solutions for nonlocal equations with critical nonlinearity
Mousomi Bhakta, Patrizia Pucci
This paper deals with existence and multiplicity of positive solutions to the following class of nonlocal equations with critical nonlinearity: \begin{equation} \tag{}…
Existence and Multiplicity of positive solutions of certain nonlocal scalar field equations
Mousomi Bhakta, Souptik Chakraborty, Debdip Ganguly
We study existence and multiplicity of positive solutions of the following class of nonlocal scalar field equations: \begin{equation} \tag{} \left\{\begin{aligned} (-Δ…
Integral representation using Green function for fractional Hardy equation
Mousomi Bhakta, Anup Biswas, Debdip Ganguly +1
Our main aim is to study Green function for the fractional Hardy operator in , where and is the best constant in…
On the existence and multiplicity of solutions to fractional Lane-Emden elliptic systems involving measures
Mousomi Bhakta, Phuoc-Tai Nguyen
We study positive solutions to the fractional Lane-Emden system \begin{equation*} \tag{S}\label{S} \left\{ \begin{aligned} (-Δ)^s u &= v^p+μ\quad &&\text{in } Ω\\ (-Δ)^s v &= u^q+ν…
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, &…