10 papers · 1 filter
On removable singular sets for solutions of higher order differential inequalities
A. A. Kon'kov, A. E. Shishkov
We obtain conditions guaranteeing that weak solutions of the differential inequality $$ \sum_{|α| = m} \partial^α a_α(x, u) \ge f (x) g (|u|) \quad \mbox{in } Ω\setminus S, $$ has…
On large time behavior of solutions of higher order evolution inequalities with fast diffusion
A. A. Kon'kov, A. E. Shishkov
We obtain stabilization conditions and large time estimates for weak solutions of the inequality $$ \sum_{|α| = m} \partial^α a_α(x, t, u) - u_t \ge f (x, t) g (u) \quad \mbox{in }…
On the existence of solutions of the second boundary value problem for -Laplacian on Riemannian manifolds
V. V. Brovkin, A. A. Kon'kov
We obtain necessary and sufficient existence conditions for solutions of the boundary value problem $$ Δ_p u = f \quad \mbox{on } M, \quad \left. \left| \nabla u \right|^{p - 2} \f…
On removable singularities of solutions of higher order differential inequalities
A. A. Kon'kov, A. E. Shishkov
We obtain sufficient conditions for solutions of the th-order differential inequality $$ \sum_{|α| = m} \partial^αa_α(x, u) \ge f (x) g (|u|) \quad \mbox{in } B_1 \setminus \{ 0…
On the behavior of solutions of quasilinear elliptic inequalities near a boundary point
A. A. Kon'kov
Assume that and are real numbers and is a non-empty open subset of , . We consider the inequality $$ {\rm div} \, A (x, D u)…
Generalization of the Keller-Osserman theorem for higher order differential inequalities
A. A. Kon'kov, A. E. Shishkov
We obtain exact conditions guaranteeing that any global weak solution of the differential inequality $$ \sum_{|α| = m} \partial^α a_α(x, u) \ge g (|u|) \quad \mbox{in } {\mathbb R}…