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- W3025810317 abstract "Abstract We obtain sufficient conditions for solutions of the m th-order differential inequality <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:munder> <m:mo largeop=true movablelimits=false symmetric=true>∑</m:mo> <m:mrow> <m:mrow> <m:mo stretchy=false>|</m:mo> <m:mi>α</m:mi> <m:mo stretchy=false>|</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mi>m</m:mi> </m:mrow> </m:munder> <m:mrow> <m:mrow> <m:msup> <m:mo>∂</m:mo> <m:mi>α</m:mi> </m:msup> <m:mo></m:mo> <m:msub> <m:mi>a</m:mi> <m:mi>α</m:mi> </m:msub> </m:mrow> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>x</m:mi> <m:mo>,</m:mo> <m:mi>u</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> <m:mo>≥</m:mo> <m:mrow> <m:mrow> <m:mi>f</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mo></m:mo> <m:mi>g</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mo stretchy=false>|</m:mo> <m:mi>u</m:mi> <m:mo stretchy=false>|</m:mo> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo mathvariant=italic separator=true> </m:mo> <m:mrow> <m:mrow> <m:mtext>in </m:mtext> <m:mo></m:mo> <m:msub> <m:mi>B</m:mi> <m:mn>1</m:mn> </m:msub> </m:mrow> <m:mo>∖</m:mo> <m:mrow> <m:mo stretchy=false>{</m:mo> <m:mn>0</m:mn> <m:mo stretchy=false>}</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:mrow> </m:math> sum_{|alpha|=m}partial^{alpha}a_{alpha}(x,u)geq f(x)g(|u|)quadtext{in % }B_{1}setminus{0} to have a removable singularity at zero, where <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi>a</m:mi> <m:mi>α</m:mi> </m:msub> </m:math> {a_{alpha}} , f , and g are some functions, and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msub> <m:mi>B</m:mi> <m:mn>1</m:mn> </m:msub> <m:mo>=</m:mo> <m:mrow> <m:mo stretchy=false>{</m:mo> <m:mi>x</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mrow> <m:mo stretchy=false>|</m:mo> <m:mi>x</m:mi> <m:mo stretchy=false>|</m:mo> </m:mrow> <m:mo><</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mo stretchy=false>}</m:mo> </m:mrow> </m:mrow> </m:math> {B_{1}={x:|x|<1}} is a unit ball in <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> </m:math> {{mathbb{R}}^{n}} . We show in some examples the sharpness of these conditions." @default.
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- W3025810317 date "2020-04-17" @default.
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- W3025810317 title "On Removable Singularities of Solutions of Higher-Order Differential Inequalities" @default.
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- W3025810317 doi "https://doi.org/10.1515/ans-2020-2085" @default.
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