7 papers
Multiplicity Results for Mixed Local Nonlocal Equations With Indefinite Concave-Convex Type Nonlinearity
R. Dhanya, Jacques Giacomoni, Ritabrata Jana
In this article we examine the multiplicity of non-negative solutions to mixed local-nonlocal equations involving \((-Δ_p) + (-Δ^{s}_{q})\) in a bounded smooth domain. The nonlinea…
Interior and Boundary Regularity of Mixed Local Nonlocal Problem with Singular Data and Its Applications
R. Dhanya, Jacques Giacomoni, Ritabrata Jana
In this article, we examine the Hölder regularity of solutions to equations involving a mixed local-nonlocal nonlinear nonhomogeneous operator $\fp + \fqs$ with singular data, unde…
Fine Boundary Regularity For The Fractional (p,q)-Laplacian
R. Dhanya, Ritabrata Jana, Uttam Kumar +1
In this article, we deal with the fine boundary regularity, a weighted Hölder regularity of weak solutions to the problem involving the fractional Laplacian denoted by $(-Δ…
Positive Solutions for Fractional p- Laplace Semipositone Problem with Superlinear Growth
R. Dhanya, Ritabrata Jana, Uttam Kumar +1
We consider a semipositone problem involving the fractional Laplace operator of the form \begin{equation*} \begin{aligned} (-Δ)_p^s u &=μ( u^{r}-1) \text{ in } Ω,\\ u &>0 \text…
Symmetry and Monotonicity Property of a Solution of (p,q) Laplace Equation with Singular Term
Ritabrata Jana
This paper examines the behavior of a positive solution $u\in C^{1,α}(\BarΩ)$ of the Laplace equation with a singular term and zero Dirichlet boundary condition. Specifical…
Strong comparison principle for a p-Laplace equation involving singularity and its applications
R. Dhanya, M. S. Indulekha, Ritabrata Jana
In this paper we prove a strong comparison principle for radially decreasing solutions $u,v\in C_{0}^{1,α}(\Bar{B_R})$ of the singular equations and $-Δ…
Proof of a Conjecture on Wiener Index and Eccentricity of a graph due to edge contraction
Joyentanuj Das, Ritabrata Jana
For a connected graph , the Wiener index, denoted by , is the sum of the distance of all pairs of distinct vertices and the eccentricity, denoted by , is t…