On Removable Singularities of Solutions of Higher-Order Differential Inequalities

Abstract

Abstract We obtain sufficient conditions for solutions of the mth-order differential inequality ∑ | α | = m ∂ α ⁡ a α ⁢ ( x , u ) ≥ f ⁢ ( x ) ⁢ g ⁢ ( | u | )   in  ⁢ B 1 ∖ { 0 } \sum_{|\alpha|=m}\partial^{\alpha}a_{\alpha}(x,u)\geq f(x)g(|u|)\quad\text{in % }B_{1}\setminus\{0\} to have a removable singularity at zero, where a α {a_{\alpha}} , f, and g are some functions, and B 1 = { x : | x | < 1 } {B_{1}=\{x:|x|<1\}} is a unit ball in ℝ n {{\mathbb{R}}^{n}} . We show in some examples the sharpness of these conditions.