Andrey Shishkov

activity

20102024

collaborators

3 papers

math.AP2024

On global solutions of quasilinear second-order elliptic inequalities

A. A. Kon'kov, A. E. Shishkov

We consider the inequality $$ - \operatorname{div} A (x, \nabla u) \ge f (u) \quad \mbox{in } {\mathbb R}^n, $$ where $n \geq 2$ and $A$ is a Caratheodory function such that $$ C_1…

math.AP2023

On a Dini type blow-up condition for nonlinear higher order differential inequalities

A. A. Kon'kov, A. E. Shishkov

We obtain a Dini type blow-up condition for global weak solutions of the differential inequality $$ \sum_{|α| = m} \partial^α a_α(x, u) \ge g (|u|) \quad \mbox{in } {\mathbb R}^n,…

math.AP2010

Singular solutions to the heat equations with nonlinear absorption and Hardy potentials

Vitali Liskevich, Andrey Shishkov, Zeev Sobol

We study the existence and nonexistence of singular solutions to the equation $u_{t} - Δ u - \frac{κ}{∣ x ∣ ^{2}} u + ∣ x ∣^{α} u ∣ u ∣^{p - 1} = 0$ , $p > 1$ , in $R^{N} \times [0, \infty)$ , $N \geq 3$ , with a singul…