3 citations · 6 across the 9 of their papers we have counts for
10 papers
On a fractional system of NLS-KDV equations with Hardy potentials
Rohit Kumar, Tuhina Mukherjee, Abhishek Sarkar
In this article, our main concern is to study the existence of bound and ground state solutions for the following fractional system of nonlinear Schrödinger-Korteweg-De Vries (NLS-…
Multiple solutions for a weighted -Laplacian problem
Rohit Kumar, Abhishek Sarkar
We prove the existence of at least three solutions for a weighted -Laplacian operator involving Dirichlet boundary condition in a weighted Sobolev space. The main tool we use he…
On the fourth order semipositone problem in
Nirjan Biswas, Ujjal Das, Abhishek Sarkar
For and , 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…
Cohomology of Lie algebroids over topological ringed spaces
Abhishek Sarkar
We consider Lie algebroids over a topological ringed space as quasicoherent sheaves of Lie-Rinehart algebras. We express hypercohomology for a locally free Lie algebroid (not neces…
On Lie algebroid over algebraic spaces
Ashis Mandal, Abhishek Sarkar
We consider Lie algebroids over algebraic spaces (in short we call it as -spaces) by considering the sheaf of Lie-Rinehart algebras. We discuss about properties of universal env…
On the eigenvalue problem involving the weighted -Laplacian in radially symmetric domains
Pavel Drábek, Ky Ho, Abhishek Sarkar
We investigate the following eigenvalue problem \begin{align*} \begin{cases} -\operatorname{div}\left( L(x) |\nabla u| ^{p-2}\nabla u\right)=λK(x)|u|^{p-2}u \quad \text{in } A_{R_1…
On the Generalized Hardy-Rellich Inequalities
T. V. Anoop, Ujjal Das, Abhishek Sarkar
In this article, we look for the weight functions (say ) that admits the following generalized Hardy-Rellich type inequality: $ \int_Ω g(x) u^2 dx \leq C \int_Ω |Δu|^2 dx, \fora…
The Fredholm alternative for the -Laplacian in exterior domains
Pavel Drabek, Ky Ho, Abhishek Sarkar
We investigate the Fredholm alternative for the -Laplacian in an exterior domain which is the complement of the closed unit ball in (). By employing tech…
Existence and Multiplicity of a Nonhomogeneous Polyharmonic Equation With Critical Exponential Growth in Even Dimension
Abhishek Sarkar
In this paper we study the existence of at least two positive weak solutions for an inhomogeneous fourth order equation with Navier boundary data involving nonlinearities of critic…
Isolated Singularities of Polyharmonic Operator in Even Dimension
Dhanya Rajendran, Abhishek Sarkar
We consider the equation in the sense of distribution in where and Then it is known that solves $Δ^2 u=g(x,u)+αδ_…