On the asymptotic behavior of solutions of Emden–Fowler equations on time scales

Consider the Emden-Fowler dynamic equation where is the quotient of odd positive integers, and denotes a time scale which is unbounded above and satisfies an additional condition (C) given below. We prove that if (and when α  = 1 we also assume lim t →∞ tp ( t ) μ ( t ) = 0), then (0.1) has a soluti...

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Bibliographic Details
Published inAnnali di matematica pura ed applicata Vol. 191; no. 2; pp. 205 - 217
Main Authors Erbe, Lynn, Baoguo, Jia, Peterson, Allan
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.05.2012
Springer Nature B.V
Subjects
Asymptotic properties
Mathematics
Mathematics and Statistics
Quotients
Emden-Fowler equation
39A99
39A10
34N05
Asymptotic behavior
Generalized Gronwall’s Inequality
34K11
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Summary:Consider the Emden-Fowler dynamic equation where is the quotient of odd positive integers, and denotes a time scale which is unbounded above and satisfies an additional condition (C) given below. We prove that if (and when α  = 1 we also assume lim t →∞ tp ( t ) μ ( t ) = 0), then (0.1) has a solution x ( t ) with the property that
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-010-0179-5