Genival da Silva

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math.AP2026

An equation involving the 1-Laplacian and a singular nonlinearity

Genival da Silva

We prove existence of solutions to a nonlinear degenerate elliptic equation of the form \[ \begin{cases} -Î_{1} u+ \frac{|D u|}{(1-u)^Î³}=g & \mbox{in $I^c ◯$ ,}\\ u=0 \hfill & \mbox{…

math.AP2024

An inhomogeneous p-laplacian equation with a Hardy potential

Genival da Silva

In this work we study the existence and regularity of solutions to the following equation: $- I^_{p} u + g (x) u = \frac{I ^}{»} ∣ x ∣^{p} ∣ u ∣^{p - 2} u + f,$ where $1 < p < N$ and $f \in L^{m}$ ,…

math.AP2024

On a fully nonlinear k-Hessian system of Lane-Emden type

Genival da Silva

In this manuscript we prove the existence of solutions to a fully nonlinear system of (degenerate) elliptic equations of Lane-Emden type and discuss a inhomogeneous generalization.