Marius Ghergu

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20242026

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math.AP2025

Isolated singularities for elliptic equations with convolution terms in a punctured ball

Marius Ghergu, Zhe Yu

The purpose of this article is two-fold. First, we investigate the inequality $$ -Δu+V(x) u\geq f\quad\mbox{ in } B_1\setminus\{0\}\subset \mathbb{R}^N , N \geq 2, $$ where $f\in L…

math.AP2025

The Gierer-Meinhardt system in the entire space with non-local proliferation rates

Marius Ghergu, Nikos I. Kavallaris, Yasuhito Miyamoto

In this work, we present a novel stationary Gierer-Meinhardt system incorporating non-local proliferation rates, defined as follows: $$ \begin{cases} \displaystyle -Δu+λu=\frac{J*u…

math.AP2025

Superharmonic functions in the upper half space with a nonlocal boundary condition

Marius Ghergu

We discuss the existence of positive superharmonic functions $u$ in $R_{+}^{N} = R^{N - 1} \times (0, \infty)$ , $N \geq 3$ , in the sense $- Δ u = μ$ for some Radon measure $μ$ ,…