8 papers
Global branching for semilinear fractional Laplace with sublinear nonlinearity
Jefferson Abrantes, Rohit Kumar, Abhishek Sarkar
This article investigates the existence, nonexistence, and multiplicity of positive solutions to the sublinear fractional elliptic problem . We begin by establishing sever…
Principal eigenvalues for the weighted p-Laplacian and antimaximum principle in
Anumol Joseph, Abhishek Sarkar
We study the existence of principal eigenvalues and principal eigenfunctions for weighted eigenvalue problems of the form: \begin{equation*} - \mbox{div} ( L (x) |\nabla u|^{p-2} \…
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 . A sharp singular concentration-compactness principle, improving…
On the study of -Laplace Choquard equations with critical Trudinger-Moser nonlinearity in
Deepak Kumar Mahanta, Tuhina Mukherjee, Abhishek Sarkar +1
This paper deals with the existence and multiplicity of nontrivial solutions for -Laplace equations with the Stein-Weiss reaction under critical exponential nonlinearity in…
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 associated with the fractional -Laplace operator. To be precise, we want to…
Degenerate Schr{ö}dinger-Kirchhoff -Laplacian problem With singular Trudinger-Moser nonlinearity in
Deepak Kumar Mahanta, Tuhina Mukherjee, Abhishek Sarkar
In this paper, we deal with the existence of nontrivial nonnegative solutions for a -Laplacian Schr{ö}dinger-Kirchhoff problem in with singular exponential n…
Characterizations of compactness and weighted eigenvalue problem associated with fractional Hardy-type inequalities
Ujjal Das, Rohit Kumar, Abhishek Sarkar
In this article, we consider the following fractional {Hardy-type} inequality: \begin{align} \label{Fractional Hardy_abst} \int_{\mathbb{R}^N} |w(x)||u(x)|^p \mathrm{d}x \leq C \in…
On critically coupled (s_1, s_2)-fractional system of Schrödinger equations with Hardy potential
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 Schrödinger equations with Hardy potentials:…