Abhishek Sarkar

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20222025

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math.AP2024

A Note on Sharpened Singular Adams-Type Inequalities

Deepak Kumar Mahanta, Tuhina Mukherjee, Abhishek Sarkar

We establish a sharp Adams-type inequality in higher-order function spaces with singular weights on $R^{n}$ . A sharp singular concentration-compactness principle, improving…

math.AP2024

On the study of $(p, Q)$ -Laplace Choquard equations with critical Trudinger-Moser nonlinearity in $H^{N}$

Deepak Kumar Mahanta, Tuhina Mukherjee, Abhishek Sarkar +1

This paper deals with the existence and multiplicity of nontrivial solutions for $(p, Q)$ -Laplace equations with the Stein-Weiss reaction under critical exponential nonlinearity in…

math.AP2024

Existence of Positive Solutions for Generalized Fractional Brézis-Nirenberg Problem

Rohit Kumar, Abhishek Sarkar

In this article, we study the fractional Brézis-Nirenberg type problem on whole domain $R^{N}$ associated with the fractional $p$ -Laplace operator. To be precise, we want to…

A Note on Sharpened Singular Adams-Type Inequalities

On the study of (p,Q)-Laplace Choquard equations with critical Trudinger-Moser nonlinearity in HN

Existence of Positive Solutions for Generalized Fractional Brézis-Nirenberg Problem

On the study of $(p, Q)$ -Laplace Choquard equations with critical Trudinger-Moser nonlinearity in $H^{N}$