From the 1 of 6 linked papers with an AI index.
6 papers
Optimization for the first weighted eigenvalue of local-nonlocal operators with a potential
R. Lakshmi, Sekhar Ghosh, Ratan Kr. Giri
The paper investigates how to choose a potential function to maximize or minimize the first eigenvalue of mixed local‑nonlocal differential operators, proving existence and uniquen…
On weak and viscosity solutions to a nonhomogeneous mixed local-nonlocal equation
R. Lakshmi, Sekhar Ghosh
This paper explores the relationship between weak and viscosity solutions to a nonhomogeneous mixed local and non-local -Laplace equation in a bounded Lipschitz domain in $\math…
On equivalence of weak and viscosity solutions to nonlocal double phase problems with nonhomogeneous data
Sekhar Ghosh, R. Lakshmi, Chao Zhang
This work focuses on the nonhomogeneous nonlocal double phase problem \begin{align*} L_au(x)=f(x,u,D_s^p u, D_{a,t}^q u) \text{ in } Ω, \end{align*} where …
Brezis-Nirenberg type problems associated with nonlinear superposition operators of mixed fractional order
Yergen Aikyn, Sekhar Ghosh, Vishvesh Kumar +1
This paper aims to study the Brezis-Nirenberg type problem driven by the nonlinear superposition of operators of the form w…
Critical Equations Involving Nonlocal Subelliptic Operators on Stratified Lie Groups: Spectrum, Bifurcation and Multiplicity
Sekhar Ghosh, Vishvesh Kumar
In this paper, we explore the bifurcation phenomena and establish the existence of multiple solutions for the nonlocal subelliptic Brezis-Nirenberg problem: \begin{equation*} \begi…
Existence results for mixed local and nonlocal elliptic equations involving singularity and nonregular data
Souvik Bhowmick, Sekhar Ghosh
In this paper, we prove the existence of weak, veryweak and duality solutions to a class of elliptic problems involving singularity and measure data which is given by: $-Îu+(-Î)^…