From the 1 of 12 linked papers with an AI index.
12 papers
Regularity for the fractional logarithmic -Laplacian
Nirjan Biswas, Stuti Das, Abhrojyoti Sen
The paper establishes a Harnack inequality with tail terms and local Hölder continuity for the fractional logarithmic p‑Laplacian, a nonlocal operator obtained by differentiating t…
Harnack inequality for mixed local-nonlocal weighted homogeneous equations
Nirjan Biswas, Stuti Das
We consider the following class of mixed local-nonlocal equations: \begin{equation}\tag{P}\label{eq:P} -Î_p u + (-Î)_p^s u = V |u|^{p-2}u \text{ in } Ω, \end{equation} where $s…
Brezis-Nirenberg problems for mixed local-nonlocal operators with superlinear perturbations: compactness and applications
Mousomi Bhakta, Nirjan Biswas, Paramananda Das
In this paper, we consider the following mixed local nonlocal Brezis-Nirenberg problem \begin{equation}\label{crit_pro_abstract}\tag{} -Îu+(-Î)^s u=λ|u|^{p-2}…
Mixed local-nonlocal equations with critical nonlinearity on : Non-existence, Existence, and Multiplicity of positive solutions
Nirjan Biswas, Souptik Chakraborty, Paramananda Das
We consider the following quasilinear critical problem involving the mixed local-nonlocal operator: \begin{equation}\label{main_prob_abstract_1}\tag{} -Î_p u+(-Î_p…
Quasilinear problems with mixed local-nonlocal operator and concave-critical nonlinearities: Multiplicity of positive solutions
Mousomi Bhakta, Nirjan Biswas, Paramananda Das
We study the existence and multiplicity of positive solutions for the following concave-critical problem driven by an operator of mixed order obtained by the sum of the classical $…
Fractional -Laplace systems with critical Hardy nonlinearities: Existence and Multiplicity
Nirjan Biswas, Paramananda Das, Shilpa Gupta
Let be a bounded open set containing zero, and . In this paper, we first deal with the existence, non-existence and some p…