Nonoscillation theorems for second order nonlinear differential equations

James S. W. Wong

doi:10.1090/s0002-9939-99-05036-4

Nonoscillation theorems for second order nonlinear differential equations

James S. W. Wong

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

8 Citations (Scopus)

Abstract

We prove nonoscillation theorems for the second order Emden-Fowler equation (E): y″ + a(x)|y|^γ-1y = 0, γ > 0, where a(x) a(x) ε C(0,∞) and γ ≠ 1. It is shown that when x(γ+3)/2+δ a(x) is nondecreasing for any δ > 0 and is bounded above, then (E) is nonoscillatory. This improves a well-known result of Belohorec in the sublinear case, i.e. when 0 < γ < 1 and 0 < δ < (1 - γ)/2. © 1999 American Mathematical Society.

Original language	English
Pages (from-to)	1387-1395
Journal	Proceedings of the American Mathematical Society
Volume	127
Issue number	5
DOIs	https://doi.org/10.1090/s0002-9939-99-05036-4
Publication status	Published - 1999
Externally published	Yes

Bibliographical note

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 equations
Oscillation
Second order

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title = "Nonoscillation theorems for second order nonlinear differential equations",

abstract = "We prove nonoscillation theorems for the second order Emden-Fowler equation (E): y″ + a(x)|y|γ-1y = 0, γ > 0, where a(x) a(x) ε C(0,∞) and γ ≠ 1. It is shown that when x(γ+3)/2+δ a(x) is nondecreasing for any δ > 0 and is bounded above, then (E) is nonoscillatory. This improves a well-known result of Belohorec in the sublinear case, i.e. when 0 < γ < 1 and 0 < δ < (1 - γ)/2. {\textcopyright} 1999 American Mathematical Society.",

keywords = "Asymptotic behavior, Nonlinear, Ordinary differential equations, Oscillation, Second order",

author = "Wong, \{James S. W.\}",

note = "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].",

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doi = "10.1090/s0002-9939-99-05036-4",

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pages = "1387--1395",

journal = "Proceedings of the American Mathematical Society",

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TY - JOUR

T1 - Nonoscillation theorems for second order nonlinear differential 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 - 1999

Y1 - 1999

N2 - We prove nonoscillation theorems for the second order Emden-Fowler equation (E): y″ + a(x)|y|γ-1y = 0, γ > 0, where a(x) a(x) ε C(0,∞) and γ ≠ 1. It is shown that when x(γ+3)/2+δ a(x) is nondecreasing for any δ > 0 and is bounded above, then (E) is nonoscillatory. This improves a well-known result of Belohorec in the sublinear case, i.e. when 0 < γ < 1 and 0 < δ < (1 - γ)/2. © 1999 American Mathematical Society.

AB - We prove nonoscillation theorems for the second order Emden-Fowler equation (E): y″ + a(x)|y|γ-1y = 0, γ > 0, where a(x) a(x) ε C(0,∞) and γ ≠ 1. It is shown that when x(γ+3)/2+δ a(x) is nondecreasing for any δ > 0 and is bounded above, then (E) is nonoscillatory. This improves a well-known result of Belohorec in the sublinear case, i.e. when 0 < γ < 1 and 0 < δ < (1 - γ)/2. © 1999 American Mathematical Society.

KW - Asymptotic behavior

KW - Nonlinear

KW - Ordinary differential equations

KW - Oscillation

KW - Second order

UR - https://www.scopus.com/pages/publications/22644448419

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-22644448419&origin=recordpage

U2 - 10.1090/s0002-9939-99-05036-4

DO - 10.1090/s0002-9939-99-05036-4

M3 - RGC 21 - Publication in refereed journal

SN - 0002-9939

VL - 127

SP - 1387

EP - 1395

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 5

ER -

Nonoscillation theorems for second order nonlinear differential equations

Abstract

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Research Keywords

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