Nirjan Biswas

activity

20182026

most citedOn the optimization of the first weighted eigenvalue

10 citations · 37 across the 21 of their papers we have counts for

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21 papers · 1 filter

math.AP2026

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

Nirjan Biswas, Souptik Chakraborty, Debangana Mukherjee

We study the critical fractional $p$ -Hardy-Sobolev equation \begin{equation}\tag{ $P$ }\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

Regularity for the fractional logarithmic $p$ -Laplacian

Nirjan Biswas, Stuti Das, Abhrojyoti Sen

We prove the Harnack inequality (with tails) and local Hölder regularity for the fractional logarithmic $p$ -Laplace operator, which is derived by differentiating the fractional $p$ …

math.AP2026

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{ $P_{2^{*}}$ } -Δu+(-Δ)^s u=λ|u|^{p-2}u+|…

math.AP2026

Harnack inequality for mixed local-nonlocal weighted homogeneous equations

Nirjan Biswas, Stuti Das

We consider the following class of mixed local-nonlocal equations: \begin{equation}\tag{P}\label{eq:P} -Δ_p u + (-Δ)_p^s u = V |u|^{p-2}u \text{ in } Ω, \end{equation} where $s \in…

math.AP2026

Global compactness results for fractional $p$ -Laplace Hardy Sobolev operator on a bounded domain

Nirjan Biswas

In this paper, we establish a Struwe type global compactness result for a class of nonlinear critical Hardy-Sobolev exponent problems driven by the fractional $p$ -Laplace Hardy-Sob…

math.AP2025

Mixed local-nonlocal equations with critical nonlinearity on $R^{N}$ : 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{ $P_{p}$ } -Δ_p u+(-Δ_p)^…

math.AP2025

Fractional $p$ -Laplace systems with critical Hardy nonlinearities: Existence and Multiplicity

Nirjan Biswas, Paramananda Das, Shilpa Gupta

Let $Ω \subset R^{d}$ be a bounded open set containing zero, $s \in (0, 1)$ and $p \in (1, \infty)$ . In this paper, we first deal with the existence, non-existence and some pr…

math.AP2025

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 $…

math.AP2025

On the linear independence condition for the Bobkov-Tanaka first eigenvalue of the double-phase operator

Nirjan Biswas, Laura Gambera, Umberto Guarnotta

The paper investigates a pivotal condition for the Bobkov-Tanaka type spectrum for double-phase operators. This condition is satisfied if either the weight $w$ driving the double-p…

math.AP2025★ 1 cited

On $p$ -fractional weakly-coupled system with critical nonlinearities

Nirjan Biswas, Souptik Chakraborty

This paper deals with the following nonlocal system of equations: \begin{equation}\tag{ $S$ }\label{MAT1} (-Δ_p)^s u = \fracα{p_s^*}|u|^{α-2}u|v|^β+f(x) \text{ in } \mathbb{…

math.AP2024★ 1 cited

Higher order fractional weighted homogeneous spaces: characterization and finer embeddings

Nirjan Biswas, Rohit Kumar

In this article, for $N \geq 2, s \in (1, 2), p \in (1, \frac{N}{s}), σ = s - 1$ and $a \in [0, \frac{N - s p}{2})$ , we establish an isometric isomorphism between the higher order fraction…

math.AP2023★ 1 cited

Strict Faber-Krahn type inequality for the mixed local-nonlocal operator under polarization

K Ashok Kumar, Nirjan Biswas

Let $Ω \subset R^{d}$ with $d \geq 2$ be a bounded domain of class $C^{1, β}$ for some $β \in (0, 1)$ . For $p \in (1, \infty)$ and $s \in (0, 1)$ , let $Λ_{p}^{s} (Ω)$ be the…

math.AP2023★ 8 cited

Study of fractional semipositone problems on $R^{N}$

Nirjan Biswas

Let $s \in (0, 1)$ and $N > 2 s$ . In this paper, we consider the following class of nonlocal semipositone problems: \begin{align*} (-Δ)^s u= g(x)f_a(u) \text { in } \mathbb{R}^N, \; u…

math.AP2023★ 1 cited

Lipschitz potential estimates for diffusion with jumps

Nirjan Biswas, Harsh Prasad

For $p \in (1, \infty)$ and $s \in (0, 1)$ , we consider the following mixed local-nonlocal equation $- Δ_{p} u + (- Δ_{p})^{s} u = f in Ω,$ where $Ω \subset R^{d}$ is…

math.AP2023★ 2 cited

Strict monotonicity of the first $q$ -eigenvalue of the fractional $p$ -Laplace operator over annuli

K Ashok Kumar, Nirjan Biswas

Let $B, B^{'} \subset R^{d}$ with $d \geq 2$ be two balls such that $B^{'} \subset\subset B$ and the position of $B^{'}$ is varied within $B$ . For $p \in (1, \infty),$ $s \in (0, 1)$ , an…

math.AP2022★ 6 cited

On generalized eigenvalue problems of fractional $(p, q)$ -Laplace operator with two parameters

Nirjan Biswas, Firoj Sk

For $s_{1}, s_{2} \in (0, 1)$ and $p, q \in (1, \infty)$ , we study the following nonlinear Dirichlet eigenvalue problem with parameters $α, β \in R$ driven by the sum of two nonloca…

math.AP2022★ 1 cited

On the fourth order semipositone problem in $R^{N}$

Nirjan Biswas, Ujjal Das, Abhishek Sarkar

For $N \geq 5$ and $a > 0$ , we consider the following semipositone problem \begin{align*} Δ^2 u= g(x)f_a(u) \text { in } \mathbb{R}^N, \, \text{ and } \, u \in \mathcal{D}^{2,2}(\mat…

math.AP2021★ 10 cited

On the optimization of the first weighted eigenvalue

Nirjan Biswas, Ujjal Das, Mrityunjoy Ghosh

For $N \geq 2$ , a bounded smooth domain $Ω$ in $R^{N}$ , and $g_{0}, V_{0} \in L_{l oc}^{1} (Ω)$ , we study the optimization of the first eigenvalue for the following weighted eigenval…

math.AP2020★ 3 cited

Admissible function spaces for weighted Sobolev inequalities

T. V. Anoop, Nirjan Biswas, Ujjal Das

Let $k, N \in N$ with $1 \leq k \leq N$ and let $Ω = Ω_{1} \times Ω_{2}$ be an open set in $R^{k} \times R^{N - k}$ . For $p \in (1, \infty)$ and $q \in (0, \infty),$ we co…

math.AP2020

On global bifurcation for the nonlinear Steklov problems

T. V. Anoop, Nirjan Biswas

For $p \in (1, \infty),$ for an integer $N \geq 2$ and for a bounded Lipschitz domain $Ω$ , we consider the following nonlinear Steklov bifurcation problem \begin{equation*} \begin{…

math.AP2018★ 3 cited

Neumann eigenvalue problems on the exterior domains

T. V. Anoop, Nirjan Biswas

For $p \in (1, \infty)$ , we consider the following weighted Neumann eigenvalue problem on $B_{1}^{c}$ , the exterior of the closed unit ball in $R^{N}$ : \begin{equation}\label{Neumann eqn…

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

Regularity for the fractional logarithmic p-Laplacian

Brezis-Nirenberg problems for mixed local-nonlocal operators with superlinear perturbations: compactness and applications

Harnack inequality for mixed local-nonlocal weighted homogeneous equations

Global compactness results for fractional p-Laplace Hardy Sobolev operator on a bounded domain

Mixed local-nonlocal equations with critical nonlinearity on RN: Non-existence, Existence, and Multiplicity of positive solutions

Fractional p-Laplace systems with critical Hardy nonlinearities: Existence and Multiplicity

Quasilinear problems with mixed local-nonlocal operator and concave-critical nonlinearities: Multiplicity of positive solutions

On the linear independence condition for the Bobkov-Tanaka first eigenvalue of the double-phase operator

On p-fractional weakly-coupled system with critical nonlinearities

Higher order fractional weighted homogeneous spaces: characterization and finer embeddings

Strict Faber-Krahn type inequality for the mixed local-nonlocal operator under polarization

Study of fractional semipositone problems on RN

Lipschitz potential estimates for diffusion with jumps

Strict monotonicity of the first q-eigenvalue of the fractional p-Laplace operator over annuli

On generalized eigenvalue problems of fractional (p,q)-Laplace operator with two parameters

On the fourth order semipositone problem in RN

On the optimization of the first weighted eigenvalue

Admissible function spaces for weighted Sobolev inequalities

On global bifurcation for the nonlinear Steklov problems

Neumann eigenvalue problems on the exterior domains

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

Regularity for the fractional logarithmic $p$ -Laplacian

Global compactness results for fractional $p$ -Laplace Hardy Sobolev operator on a bounded domain

Mixed local-nonlocal equations with critical nonlinearity on $R^{N}$ : Non-existence, Existence, and Multiplicity of positive solutions

Fractional $p$ -Laplace systems with critical Hardy nonlinearities: Existence and Multiplicity

On $p$ -fractional weakly-coupled system with critical nonlinearities

Study of fractional semipositone problems on $R^{N}$

Strict monotonicity of the first $q$ -eigenvalue of the fractional $p$ -Laplace operator over annuli

On generalized eigenvalue problems of fractional $(p, q)$ -Laplace operator with two parameters

On the fourth order semipositone problem in $R^{N}$