A nonoscillation theorem for Emden-Fowler equations

James S.W. Wong

doi:10.1016/S0022-247X(02)00357-8

A nonoscillation theorem for Emden-Fowler equations

James S.W. Wong

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

15 Citations (Scopus)

Abstract

We study the second order Emden-Fowler equation (E) y″ + a(x) y ^γ-1 y=0, γ > 0 where a(x) is positive and absolutely continuous on (0, ∞). Let ψ(x) = x^(γ+3)^/2+δ where δ is any positive number. Theorem. Let γ ≠ 1. If ψ (x) satisfies (a) lim_x→∞ ψ (x) = k > 0 and (b) ∫^∞Ιψ′(x)Ι dx < ∞, then Eq. (E) is nonoscillatory. © 2002 Elsevier Science (USA). All rights reserved.

Original language	English
Pages (from-to)	746-754
Journal	Journal of Mathematical Analysis and Applications
Volume	274
Issue number	2
DOIs	https://doi.org/10.1016/S0022-247X(02)00357-8
Publication status	Published - 15 Oct 2002
Externally published	Yes

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Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Asymptotic behavior
Nonlinear
Ordinary differential equation
Oscillation
Second order

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title = "A nonoscillation theorem for Emden-Fowler equations",

abstract = "We study the second order Emden-Fowler equation (E) y″ + a(x) y γ-1 y=0, γ > 0 where a(x) is positive and absolutely continuous on (0, ∞). Let ψ(x) = x(γ+3)/2+δ where δ is any positive number. Theorem. Let γ ≠ 1. If ψ (x) satisfies (a) limx→∞ ψ (x) = k > 0 and (b) ∫∞Ιψ′(x)Ι dx < ∞, then Eq. (E) is nonoscillatory. {\textcopyright} 2002 Elsevier Science (USA). All rights reserved.",

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TY - JOUR

T1 - A nonoscillation theorem for Emden-Fowler equations

AU - Wong, James S.W.

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2002/10/15

Y1 - 2002/10/15

N2 - We study the second order Emden-Fowler equation (E) y″ + a(x) y γ-1 y=0, γ > 0 where a(x) is positive and absolutely continuous on (0, ∞). Let ψ(x) = x(γ+3)/2+δ where δ is any positive number. Theorem. Let γ ≠ 1. If ψ (x) satisfies (a) limx→∞ ψ (x) = k > 0 and (b) ∫∞Ιψ′(x)Ι dx < ∞, then Eq. (E) is nonoscillatory. © 2002 Elsevier Science (USA). All rights reserved.

AB - We study the second order Emden-Fowler equation (E) y″ + a(x) y γ-1 y=0, γ > 0 where a(x) is positive and absolutely continuous on (0, ∞). Let ψ(x) = x(γ+3)/2+δ where δ is any positive number. Theorem. Let γ ≠ 1. If ψ (x) satisfies (a) limx→∞ ψ (x) = k > 0 and (b) ∫∞Ιψ′(x)Ι dx < ∞, then Eq. (E) is nonoscillatory. © 2002 Elsevier Science (USA). All rights reserved.

KW - Asymptotic behavior

KW - Nonlinear

KW - Ordinary differential equation

KW - Oscillation

KW - Second order

UR - https://www.scopus.com/pages/publications/0037110118

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0037110118&origin=recordpage

U2 - 10.1016/S0022-247X(02)00357-8

DO - 10.1016/S0022-247X(02)00357-8

M3 - RGC 21 - Publication in refereed journal

SN - 0022-247X

VL - 274

SP - 746

EP - 754

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

A nonoscillation theorem for Emden-Fowler equations

Abstract

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Research Keywords

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