6 papers
Multiplicity of solutions to a class of degenerate elliptic equations in both sub-critical and critical cases
Kaushik Bal, Sanjit Biswas
Given a smooth, bounded domain , we establish the existence of two non-trivial, non-negative solutions to the semilinear degenerate elliptic equation \begin{…
Local Existence, Uniqueness, Regularity, and Global Behavior of Evolution Equations Involving Mixed Local and Nonlocal Operators
Abdelhamid Gouasmia, Hichem Hajaiej, Kaushik Bal
In this work, we address a parabolic problem featuring a potentially doubly nonlinear term, governed by a combination of local and nonlocal operators (see Problem P1 below). We fir…
On some Elliptic and Parabolic Problems Involving the Anisotropic -Laplacian
Kaushik Bal, Shilpa Gupta
We investigate a class of elliptic and parabolic partial differential equations driven by p(u) laplacian. This dependence necessitates the use of variable exponent Sobolev spaces s…
Comparison principle for Singular Fractional Laplacian Problems
Abdelhamid Gouasmia, Kaushik Bal
In this paper, we establish a novel comparison principle of independent interest and prove the uniqueness of weak solutions within the local Orlicz--Sobolev space framework, for th…
Regularity results for a class of mixed local and nonlocal singular problems involving distance function
Kaushik Bal, Stuti Das
We investigate the following mixed local and nonlocal quasilinear equation with singularity given by \begin{eqnarray*} \begin{split} -Î_pu+(-Î)_q^s u&=\frac{f(x)}{u^δ}\text { in…
Global stability and optimal control in a single-strain dengue model with fractional-order transmission and recovery process
Tahajuddin Sk, Kaushik Bal, Santosh Biswas +1
The current manuscript introduce a single-strain dengue model developed from stochastic processes incorporating fractional order transmission and recovery. The fractional derivativ…