5 papers · 1 filter
On a necessary condition for removing singularities of solutions of nonlinear elliptic inequalities
A. A. Kon'kov, A. E. Shishkov
We study solutions of the differential inequality $$ Î^{m / 2} u \ge f (x) g (u) \quad \mbox{in } B_1 \setminus \{ 0 \}, $$ where is an even integer, and are som…
On blow-up conditions for solutions of systems of quasilinear second-order elliptic inequalities
A. A. Kon'kov, A. E. Shishkov
We study systems of the differential inequalities $$ \left\{ \begin{aligned} & - \operatorname{div} A_1 (x, \nabla u_1) \ge F_1 (x, u_2) & \mbox{in } {\mathbb R}^n, & - \operatorna…
On bow-up conditions for systems of higher order differential inequalities
A. A. Kon'kov, A. E. Shishkov
We consider systems of the differential inequalities $$\left\{ \begin{aligned} & \sum_{|α| = m_1} \partial^αa_α(x, u_1) \ge f_1 (u_2) & \mbox{in } {\mathbb R}^n, & \sum_{|α| =…
On the existence of global solutions of second-order quasilinear elliptic inequalities
A. A. Kon'kov, A. E. Shishkov, M. D. Surnachev
We study the existence of global positive solutions of the differential inequalities $$ - \operatorname{div} A (x, u, \nabla u) \ge f (u) \quad \mbox{in } {\mathbb R}^n, $$ where $…
On blow-up conditions for nonlinear higher order evolution inequalities
A. A. Kon'kov, A. E. Shishkov
For the problem $$ \left\{ \begin{aligned} & \partial_t^k u - \sum_{|α| = m} \partial^α a_α(x, t, u) \ge f (|u|) \quad \mbox{in } {\mathbb R}_+^{n+1} = {\mathbb R}^n \times (0,…