About: De Haan type increasing solutions of half-linear differential equations     Goto   Sponge   Distinct   Permalink

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  • We study asymptotic behavior of eventually positive increasing solutions to the half-linear equation $(r(t)|y'|^{alpha-1}sgn y')'=p(t)|y|^{alpha-1}sgn y$, where $r,p$ are positive continuous functions and $alphain(1,infty)$. We give conditions which guarantee that any such a solution is in the class $Gamma$ (in the de Haan sense). We also discuss regularly varying solutions and connections with a generalized regular variation and other related concepts. The results can be viewed as a half-linear extension of existing statements for linear equations, but in some aspects they are new also in the linear case.
  • We study asymptotic behavior of eventually positive increasing solutions to the half-linear equation $(r(t)|y'|^{alpha-1}sgn y')'=p(t)|y|^{alpha-1}sgn y$, where $r,p$ are positive continuous functions and $alphain(1,infty)$. We give conditions which guarantee that any such a solution is in the class $Gamma$ (in the de Haan sense). We also discuss regularly varying solutions and connections with a generalized regular variation and other related concepts. The results can be viewed as a half-linear extension of existing statements for linear equations, but in some aspects they are new also in the linear case. (en)
Title
  • De Haan type increasing solutions of half-linear differential equations
  • De Haan type increasing solutions of half-linear differential equations (en)
skos:prefLabel
  • De Haan type increasing solutions of half-linear differential equations
  • De Haan type increasing solutions of half-linear differential equations (en)
skos:notation
  • RIV/67985840:_____/14:00429354!RIV15-AV0-67985840
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  • I, P(GAP201/10/1032)
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  • 1
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  • RIV/67985840:_____/14:00429354
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  • half-linear equation; increasing solution; Beurling slowly varying function; class Gamma; regular variation; rapid variation (en)
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  • US - Spojené státy americké
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  • [2868180ABAC6]
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  • Journal of Mathematical Analysis and Applications
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  • 412
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  • Řehák, Pavel
http://linked.open...ain/vavai/riv/wos
  • 000330419300021
issn
  • 0022-247X
number of pages
http://bibframe.org/vocab/doi
  • 10.1016/j.jmaa.2013.10.048
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