5 papers
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…
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…