Abhishek Sarkar

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20152024

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math.AP2023

On the extreme value of Nehari manifold for nonlocal singular Schr{ö}dinger-Kirchhoff equations in $R^{N}$

Deepak Kumar Mahanta, Tuhina Mukherjee, Abhishek Sarkar

This article investigates the existence, non-existence, and multiplicity of weak solutions for a parameter-dependent nonlocal Schrödinger-Kirchhoff type problem on $R^{N}$ in…

math.AP2023

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-…

math.AP2022

Multiple solutions for a weighted $p$ -Laplacian problem

Rohit Kumar, Abhishek Sarkar

We prove the existence of at least three solutions for a weighted $p$ -Laplacian operator involving Dirichlet boundary condition in a weighted Sobolev space. The main tool we use he…

math.AP2015

Isolated Singularities of Polyharmonic Operator in Even Dimension

Dhanya Rajendran, Abhishek Sarkar

We consider the equation $Δ^{2} u = g (x, u) \geq 0$ in the sense of distribution in $Ω^{'} = Ω ∖ {0}$ where $u$ and $- Δ u \geq 0.$ Then it is known that $u$ solves $Δ^2 u=g(x,u)+αδ_…

On the extreme value of Nehari manifold for nonlocal singular Schr{ö}dinger-Kirchhoff equations in RN

On a fractional system of NLS-KDV equations with Hardy potentials

Multiple solutions for a weighted p-Laplacian problem

Isolated Singularities of Polyharmonic Operator in Even Dimension

On the extreme value of Nehari manifold for nonlocal singular Schr{ö}dinger-Kirchhoff equations in $R^{N}$

Multiple solutions for a weighted $p$ -Laplacian problem