45 citations · 173 across the 35 of their papers we have counts for
36 papers · 1 filter
On subelliptic equations on stratified Lie groups driven by singular nonlinearity and weak data
S. Sahu, D. Choudhuri, D. D. Repovš
The article is about an elliptic problem defined on a {\it stratified Lie group}. Both sub- and superlinear cases are considered whose solutions are guaranteed to exist in light of…
A multiphase eigenvalue problem on a stratified Lie group
Debajyoti Choudhuri, Leandro S. Tavares, Dušan D. Repovš
We consider a multiphase spectral problem on a stratified Lie group. We prove the existence of an eigenfunction of -eigenvalue problem on a bounded domain. Furthermore, we a…
Analysis of solution to an elliptic free boundary value problem equipped with a `bad' data
Debajyoti Choudhuri, Shengda Zeng
We will study a free boundary value problem driven by a source term which is quite {\it irregular}. In the process, we will establish a monotonicity result, and regularity of the s…
An elliptic problem of the Prandtl-Batchelor type with a singularity
Debajyoti Choudhuri, Dušan D. Repovš
We establish the existence of at least two solutions of the {\it Prandtl-Batchelor} like elliptic problem driven by a power nonlinearity and a singular term. The associated energy…
On elliptic problems with Choquard term and singular nonlinearity
Debajyoti Choudhuri, Dušan D. Repovš, Kamel Saoudi
Using variational methods, we establish the existence of infinitely many solutions to an elliptic problem driven by a Choquard term and a singular nonlinearity. We further show tha…
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents
Jiabin Zuo, Debajyoti Choudhuri, Dušan D. Repovš
We prove the existence of solutions for the following critical Choquard type problem with a variable-order fractional Laplacian and a variable singular exponent \begin{align*} \beg…
On semilinear equations with free boundary conditions on stratified Lie groups
Debajyoti Choudhuri, Dušan D. Repovš
In this paper we establish existence of a solution to a semilinear equation with free boundary conditions on stratified Lie groups. In the process, a monotonicity condition is prov…
A quick sneak-peek at the -fractional Laplacian operator
Debajyoti Choudhuri
The short note here is to give a few heuristic arguments on the weird looking fractional Laplacian operator. This is certainly going to expand the vision of a reader who is looking…
On critical variable-order Kirchhoff type problems with variable singular exponent
Jiabin Zuo, Debajyoti Choudhuri, Dušan D. Repovš
We establish a continuous embedding , where the variable exponent can be close to the critical exponent $2_{s}^*(x)=\frac{2…
A singular elliptic problem involving fractional -Laplacian and a discontinuous critical nonlinearity
Kamel Saoudi, Akasmika Panda, Debajyoti Choudhuri
In this article, we prove the existence of solutions to a nonlinear nonlocal elliptic problem with a singualrity and a discontinuous critical nonlinearity which is given as follows…
Algebraic topological techniques for elliptic problems involving fractional Laplacian
A. Panda, D. Choudhuri, A. Bahrouni
We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to…
Elliptic problem driven by different types of nonlinearities
Debajyoti Choudhuri, Dušan D. Repovš
In this paper we establish the existence and multiplicity of nontrivial solutions to the following problem \begin{align*} \begin{split} (-Δ)^{\frac{1}{2}}u+u+(\ln|\cdot|*|u|^2)&=f(…
Elliptic problem in an exterior domain driven by a singularity with a nonlocal Neumann condition
D. Choudhuri, K. Saoudi
We prove the existence of ground state solution to the following problem. \begin{align*} (-Δ)^{s}u+u&=λ|u|^{-γ-1}u+P(x)|u|^{p-1}u,~\text{in}~\mathbb{R}^N\setminusΩ\\ N_su(x)&=0,~\t…
A parabolic problem involving -Laplacian, a power and a singular nonlinearity
Akasmika Panda, Debajyoti Choudhuri, Kamel Saoudi
The purpose of this paper is to study nonlinear singular parabolic equations with - Laplacian. Precisely, we consider the following problem and discuss the existence of a non…
Existence of at least solutions to a fractional -Kirchhoff problem involving singularity and critical exponent
Sekhar Ghosh, Debajyoti Choudhuri, Alessio Fiscella
We study the existence of nonnegative solutions to the following nonlocal elliptic problem involving singularity \begin{align} \mathfrak{M}\left(\int_{Q}\frac{|u(x)-u(y)|^p}{|x-y|^…
Singular Fractional Choquard Equation with a Critical Nonlinearity and a Radon measure
Akasmika Panda, Debajyoti Choudhuri, Kamel Saoudi
This article concerns about the existence of a positive SOLA (Solutions Obtained as Limits of Approximations) for the following singular critical Choquard problem involving fractio…
Existence and Hölder regularity of infinitely many solutions to a -Kirchhoff type problem involving a singular nonlinearity without the Ambrosetti-Rabinowitz (AR) condition
Debajyoti Choudhuri
We carry out an investigation of the existence of infinitely many solutions to a fractional -Kirchhoff type problem with a singularity and a superlinear nonlinearity with a homo…
Infinitely many small solutions to an elliptic PDE of variable exponent with a singular nonlinearity
Sekhar Ghosh, Debajyoti Choudhuri, Ratan Kr. Giri
We prove the existence of infinitely many nonnegative solutions to the following nonlocal elliptic partial differential equation involving singularities \begin{align} (-Δ)_{p(\cdot…
Existence and multiplicity of solutions to a Laplacian system with a concave and singular nonlinearities
Debajyoti Choudhuri, Kamel Saoudi, Kratou Mouna
In this paper we study the existence of multiple nontrivial positive weak solutions to the following system of problems. \begin{align*} \begin{split} -Δ_{p}u-Δ_q u &= λf(x)|u|^{r-2…
A weighted fractional problem involving a singular nonlinearity and a data
Akasmika Panda, Debajyoti Choudhuri, Leandro S. Tavares
In this article, we show the existence of a unique entropy solution to the following problem: \begin{equation} \begin{split} (-Δ)_{p,α}^su&= f(x)h(u)+g(x) ~\text{in}~Ω,\\ u&>0~\tex…
A study of the Prandtl Batchelor problem using variational method
Debajyoti Choudhuri, Jiabin Zuo
In this paper, we investigate the existence of nontrivial weak solutions for the Prandtl-Batchelor type free boundary value elliptic problem driven by a power nonlinearity. The alg…
Existence of positive solutions for a singular elliptic problem with critical exponent and measure data
Akasmika Panda, Debajyoti Choudhuri, Ratan K. Giri
We prove the existence of a positive {\it SOLA (Solutions Obtained as Limits of Approximations)} to the following PDE involving fractional power of Laplacian \begin{equation} \begi…
Existence and multiplicity of solutions to a nonlocal elliptic PDE with variable exponent in a Nehari manifold using the Banach fixed point theorem
Amita Soni, D. Choudhuri
In this paper we study the existence and multiplicity of two distinct nontrivial weak solutions of the following equation in Nehari manifold. We have also proved that these solutio…
Least energy sign-changing solution of fractional -Laplacian problems involving singularities
Sekhar Ghosh, Kamel Saoudi, Mouna Kratou +1
In this paper we study the existence of a least energy sign-changing solution to a nonlocal elliptic PDE involving singularity by using the Nehari manifold method, the constraint v…