On bow-up conditions for systems of higher order differential inequalities
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915389228711936 |
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| author | Kon'kov, A. A. Shishkov, A. E. |
| author_facet | Kon'kov, A. A. Shishkov, A. E. |
| contents | We consider systems of the differential inequalities $$\left\{ \begin{aligned} & \sum_{|α| = m_1} \partial^αa_α(x, u_1) \ge f_1 (u_2) & \mbox{in } {\mathbb R}^n, & \sum_{|α| = m_2} \partial^αb_α(x, u_2) \ge f_2 (u_1) & \mbox{in } {\mathbb R}^n, \end{aligned} \right. $$ where $n, m_1, m_2 \ge 1$ are integers and $a_α$ and $b_α$ are Caratheodory functions such that $$ |a_α(x, ζ)| + |b_α(x, ζ)| \le A |ζ| $$ with some constant $A > 0$ for almost all $x \in {\mathbb R}^n$ and for all $ζ\in {\mathbb R}$. For solutions of these systems exact blow-up conditions are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10495 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On bow-up conditions for systems of higher order differential inequalities Kon'kov, A. A. Shishkov, A. E. Analysis of PDEs 35B44, 35B08, 35J30, 35J70 We consider systems of the differential inequalities $$\left\{ \begin{aligned} & \sum_{|α| = m_1} \partial^αa_α(x, u_1) \ge f_1 (u_2) & \mbox{in } {\mathbb R}^n, & \sum_{|α| = m_2} \partial^αb_α(x, u_2) \ge f_2 (u_1) & \mbox{in } {\mathbb R}^n, \end{aligned} \right. $$ where $n, m_1, m_2 \ge 1$ are integers and $a_α$ and $b_α$ are Caratheodory functions such that $$ |a_α(x, ζ)| + |b_α(x, ζ)| \le A |ζ| $$ with some constant $A > 0$ for almost all $x \in {\mathbb R}^n$ and for all $ζ\in {\mathbb R}$. For solutions of these systems exact blow-up conditions are obtained. |
| title | On bow-up conditions for systems of higher order differential inequalities |
| topic | Analysis of PDEs 35B44, 35B08, 35J30, 35J70 |
| url | https://arxiv.org/abs/2507.10495 |