8 papers · 1 filter
Existence and Multiplicity results for Weakly coupled system of Pucci's extremal operator
Karan Rathore, Mohan Mallick
In this work, we investigate the existence of multiple positive solutions for a weakly coupled system of nonlinear elliptic equations governed by Pucci extremal operators. Specific…
Shape Optimization for the Principal Eigenvalue of the Pucci Operator in Three Dimensions
Mohan Mallick, Ram Baran Verma
We investigate shape optimization for the principal eigenvalue of the Pucci extremal operator \[ \left\{ \begin{aligned} -\mathcal{M}^+_{λ,Λ}(D^{2}u)&=μ^{+}_{1}(Ω)u &&\text{in }Ω,\…
Lane--Emden Systems with Singular Nonlinearities for the Fully Nonlinear Elliptic Operator
Karan Rathore, Mohan Mallick, Ram Baran Verma
Consider \[ \begin{cases} F(D^2 u,Du,u,x) = u^{-p}v^{-q},~\text{in}~Ω\\ F(D^2 v,Dv,v,x)=u^{-r}v^{-s},~~\text{in}~~Ω\\ u,v>0~~\text{in}~~Ω\\ u=v=0~\quad~\text{on}~~\partialΩ, \end{c…
Exceptional Boundary Sets for Solutions of Fully Nonlinear Parabolic PDEs
Ram Baran Verma, Mohan Mallick
This article investigates the exceptional set of the boundary for the following problem: \begin{equation*} \begin{aligned} -\frac{\partial u}{\partial t} + \mathcal{M}_{λ,Λ}^+(D^2u…
Regularity for Fully Nonlinear Elliptic Equations with Natural Growth in Gradient and Singular Nonlinearity
Mohan Mallick, Ram Baran Verma
In this article we consider the following boundary value problem \begin{equation*}\label{abs} \left\{ \begin{aligned} F(x,u,Du,D^{2}u)+c(x)u+ p(x)u^{-α}&=0~\text{in}~Ω\\ u&=0~~\tex…
Multiplicity results for fully nonlinear elliptic equations with natural gradient growth
Mohan Mallick, Ram Baran Verma
In this paper, we prove a theorem concerning the existence of three solutions for the following boundary value problem: \begin{equation*} -\mathcal{M}_{λ,Λ}^+(D^2u)-Γ|Du|^2=f(u)~~~…
Optimal harvesting for a logistic model with grazing
Mohan Mallick, Ardra A, Sarath Sasi
We consider semi-linear elliptic equations of the following form: \begin{equation*} \left\{ \begin{aligned} -Δu &= λ[u-\dfrac{u^2}{K}-c \dfrac{u^2}{1+u^2}-h(x) u]=:λf_h(u), \quad &…
On a shape derivative formula for the Robin -Laplace eigenvalue
Ardra A, Mohan Mallick, Sarath Sasi
We obtain shape derivative formulae for the first eigenvalue of the Robin -Laplace operator. This result is used to study the variation of the first eigenvalue with respect to p…