7 citations · 9 across the 8 of their papers we have counts for
11 papers
Optimization for the first weighted eigenvalue of local-nonlocal operators with a potential
R. Lakshmi, Sekhar Ghosh, Ratan Kr. Giri
In this work, we study the optimization problem for the first eigenvalue of mixed local nonlocal operators plus a potential . We begin by investigating the existence and fundame…
A weighted eigenvalue problem for mixed local and nonlocal operators with potential
R. Lakshmi, Ratan Kr. Giri, Sekhar Ghosh
We study an {\it indefinite weighted eigenvalue problem} for an operator of {\it mixed-type} (that includes both the classical {\it -Laplacian} and the {\it fractional -Lapla…
Positive solutions of quasilinear elliptic equations with Fuchsian potentials in Wolff class
Ratan Kr. Giri, Yehuda Pinchover
Using Harnack's inequality and a scaling argument we study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point $ζ\in \partial…
Supercaloric functions for the parabolic -Laplace equation in the fast diffusion case
Ratan Kr. Giri, Juha Kinnunen, Kristian Moring
We study a generalized class of supersolutions, so-called -supercaloric functions, to the parabolic -Laplace equation. This class of functions is defined as lower semicontinu…
Positive Liouville theorem and asymptotic behaviour for -Laplacian type elliptic equations with Fuchsian potentials in Morrey space
Ratan Kr. Giri, Yehuda Pinchover
We study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point of the quasilinear elliptic equati…
Infinitely many small solutions to an elliptic PDE of variable exponent with a singular nonlinearity
Sekhar Ghosh, Debajyoti Choudhuri, Ratan Kr. Giri
We prove the existence of infinitely many nonnegative solutions to the following nonlocal elliptic partial differential equation involving singularities \begin{align} (-Δ)_{p(\cdot…
Problem involving nonlocal operator
Ratan Kr. Giri, D. Choudhuri, Amita Soni
The aim of this paper is to deal with the elliptic pdes involving a nonlinear integrodifferential operator, which are possibly degenerate and covers the case of fractional -Lapl…
On the properties of Ascent and Descent of Composition operator on Orlicz spaces
Ratan Kr. Giri, Shesadev Pradhan
Here, the composition operators on Orlicz spaces with finite ascent and descent as well as infinite ascent and descent are characterized.
Existence and Concentration Solutions for a class of elliptic PDEs involving -biharmonic Operator
Ratan Kr Giri, Debajyoti Choudhuri, Shesadev Pradhan
In this paper, we propose an existence result pertaining to a nontrivial solution to the problem \begin{align*} \Bigg\{\begin{split} & Δ^2_p u -Δ_p u + λV(x)|u|^{p-2}u = f(x,u)\,,\…
A study of second order semilinear elliptic PDE involving measures
Ratan Kr Giri, Debajyoti Choudhuri
The objective of this article is to study the boundary value problem for the general semilinear elliptic equation of second order involving functions or Radon measures with f…
A problem involving the -Laplacian operator
Ratan K. Giri, D. Choudhuri
Using a variational technique we guarantee the existence of a solution to the \emph{resonant Lane-Emden} problem , if and only if a solution…