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math.AP2026
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…
math.AP2026
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,\…
math.AP2026
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…