Oscillation criteria of second-order half-linear dynamic equations on time scales
In this paper, by using the Riccati transformation technique, chain rule and inequality A λ - λ AB λ - 1 + ( λ - 1 ) B λ ⩾ 0 , λ > 1 , where A and B are positive constants, we will establish some oscillation criteria for the second-order half-linear dynamic equation ( p ( t ) ( x Δ ( t ) ) γ ) Δ...
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| Veröffentlicht in: | Journal of computational and applied mathematics 2005-05, Vol.177 (2), p.375-387 |
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| container_title | Journal of computational and applied mathematics |
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| creator | Saker, S.H. |
| description | In this paper, by using the Riccati transformation technique, chain rule and inequality
A
λ
-
λ
AB
λ
-
1
+
(
λ
-
1
)
B
λ
⩾
0
,
λ
>
1
,
where
A and
B are positive constants, we will establish some oscillation criteria for the second-order half-linear dynamic equation
(
p
(
t
)
(
x
Δ
(
t
)
)
γ
)
Δ
+
q
(
t
)
x
γ
(
t
)
=
0
,
t
∈
[
a
,
b
]
on time scales, where
γ
>
1
is an odd positive integer. Our results not only unify the oscillation of half-linear differential and half-linear difference equations but can be applied on different types of time scales and improve some well-known results in the difference equation case. Some examples are considered here to illustrate our main results. |
| doi_str_mv | 10.1016/j.cam.2004.09.028 |
| format | Article |
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A
λ
-
λ
AB
λ
-
1
+
(
λ
-
1
)
B
λ
⩾
0
,
λ
>
1
,
where
A and
B are positive constants, we will establish some oscillation criteria for the second-order half-linear dynamic equation
(
p
(
t
)
(
x
Δ
(
t
)
)
γ
)
Δ
+
q
(
t
)
x
γ
(
t
)
=
0
,
t
∈
[
a
,
b
]
on time scales, where
γ
>
1
is an odd positive integer. Our results not only unify the oscillation of half-linear differential and half-linear difference equations but can be applied on different types of time scales and improve some well-known results in the difference equation case. Some examples are considered here to illustrate our main results.</description><identifier>ISSN: 0377-0427</identifier><identifier>EISSN: 1879-1778</identifier><identifier>DOI: 10.1016/j.cam.2004.09.028</identifier><identifier>CODEN: JCAMDI</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Exact sciences and technology ; Finite differences and functional equations ; Mathematical analysis ; Mathematics ; Ordinary differential equations ; Oscillation ; Sciences and techniques of general use ; Second-order half-linear dynamic equations ; Time scale</subject><ispartof>Journal of computational and applied mathematics, 2005-05, Vol.177 (2), p.375-387</ispartof><rights>2004</rights><rights>2005 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c389t-55174f245645b8e105b21d357531f43565ade669720e92604aeb9ecd96f65adb3</citedby><cites>FETCH-LOGICAL-c389t-55174f245645b8e105b21d357531f43565ade669720e92604aeb9ecd96f65adb3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0377042704004340$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16555044$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Saker, S.H.</creatorcontrib><title>Oscillation criteria of second-order half-linear dynamic equations on time scales</title><title>Journal of computational and applied mathematics</title><description>In this paper, by using the Riccati transformation technique, chain rule and inequality
A
λ
-
λ
AB
λ
-
1
+
(
λ
-
1
)
B
λ
⩾
0
,
λ
>
1
,
where
A and
B are positive constants, we will establish some oscillation criteria for the second-order half-linear dynamic equation
(
p
(
t
)
(
x
Δ
(
t
)
)
γ
)
Δ
+
q
(
t
)
x
γ
(
t
)
=
0
,
t
∈
[
a
,
b
]
on time scales, where
γ
>
1
is an odd positive integer. Our results not only unify the oscillation of half-linear differential and half-linear difference equations but can be applied on different types of time scales and improve some well-known results in the difference equation case. Some examples are considered here to illustrate our main results.</description><subject>Exact sciences and technology</subject><subject>Finite differences and functional equations</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Ordinary differential equations</subject><subject>Oscillation</subject><subject>Sciences and techniques of general use</subject><subject>Second-order half-linear dynamic equations</subject><subject>Time scale</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><recordid>eNqNkE1Lw0AQhhdRsFZ_gLdc9JY4m-xHFk9S_IJCEfS8bDYT3JKPdjcV-u_d2II38TSHed53mIeQawoZBSru1pk1XZYDsAxUBnl5Qma0lCqlUpanZAaFlCmwXJ6TixDWACAUZTPytgrWta0Z3dAn1rsRvTPJ0CQB7dDX6eBr9MmnaZu0dT0an9T73nTOJrjd_aRCEpOj6zAJ1rQYLslZY9qAV8c5Jx9Pj--Ll3S5en5dPCxTW5RqTDmnkjU544LxqkQKvMppXXDJC9qwggtuahRCyRxQ5QKYwUqhrZVoplVVzMntoXfjh-0Ow6g7FyzGX3ocdkHnpSx4yeU_QEEFp2UE6QG0fgjBY6M33nXG7zUFPVnWax0t68myBqWj5Zi5OZab6f3Gm9668BsUnHNgLHL3Bw6jki-HXkfv2FusnUc76npwf1z5BkxikXQ</recordid><startdate>20050515</startdate><enddate>20050515</enddate><creator>Saker, S.H.</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope><scope>L7M</scope><scope>H8D</scope></search><sort><creationdate>20050515</creationdate><title>Oscillation criteria of second-order half-linear dynamic equations on time scales</title><author>Saker, S.H.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c389t-55174f245645b8e105b21d357531f43565ade669720e92604aeb9ecd96f65adb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Exact sciences and technology</topic><topic>Finite differences and functional equations</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Ordinary differential equations</topic><topic>Oscillation</topic><topic>Sciences and techniques of general use</topic><topic>Second-order half-linear dynamic equations</topic><topic>Time scale</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Saker, S.H.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Aerospace Database</collection><jtitle>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Saker, S.H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Oscillation criteria of second-order half-linear dynamic equations on time scales</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2005-05-15</date><risdate>2005</risdate><volume>177</volume><issue>2</issue><spage>375</spage><epage>387</epage><pages>375-387</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><coden>JCAMDI</coden><abstract>In this paper, by using the Riccati transformation technique, chain rule and inequality
A
λ
-
λ
AB
λ
-
1
+
(
λ
-
1
)
B
λ
⩾
0
,
λ
>
1
,
where
A and
B are positive constants, we will establish some oscillation criteria for the second-order half-linear dynamic equation
(
p
(
t
)
(
x
Δ
(
t
)
)
γ
)
Δ
+
q
(
t
)
x
γ
(
t
)
=
0
,
t
∈
[
a
,
b
]
on time scales, where
γ
>
1
is an odd positive integer. Our results not only unify the oscillation of half-linear differential and half-linear difference equations but can be applied on different types of time scales and improve some well-known results in the difference equation case. Some examples are considered here to illustrate our main results.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cam.2004.09.028</doi><tpages>13</tpages><oa>free_for_read</oa></addata></record> |
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| issn | 0377-0427 1879-1778 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_28735857 |
| source | ScienceDirect Journals (5 years ago - present); Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Exact sciences and technology Finite differences and functional equations Mathematical analysis Mathematics Ordinary differential equations Oscillation Sciences and techniques of general use Second-order half-linear dynamic equations Time scale |
| title | Oscillation criteria of second-order half-linear dynamic equations on time scales |
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