On blow-up conditions for solutions of higher order differential inequalities

2017/11/24 by A. A. Kon’kov, Andrey Shishkov, Kon'kov, A. A. +1 · 1 citation
Mathematics · #35B08 #35B44 #35J30 #35J70 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1711.08902

openalex publication_date 2017/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

For differential inequalities of the form ∑_{|α| = m} (- 1)^m ∂^α a_α(x, u) ≥ b (x) |u|^λ in \mathbb Rⁿ, n ≥ 1, where a_α and b are some functions, we obtain conditions guaranteeing that any solution is identically equal to zero. We construct examples which show that the obtained conditions are sharp.

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• On bow-up conditions for systems of higher order differential inequalities

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