Oscillation criteria for certain second-order Emden-Fowler delay functional dynamic equations with damping on time scales
This paper is concerned with oscillations of certain second-order Emden-Fowler variable delay functional dynamic equations with damping and neutral of the form [ A ( t ) φ ( y Δ ( t ) ) ] Δ + b ( t ) φ ( y Δ ( t ) ) + P ( t ) F ( φ ( x ( δ ( t ) ) ) ) − Q ( t ) f ( φ ( x ( γ ( t ) ) ) ) = 0 on an ar...
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| Veröffentlicht in: | Advances in difference equations 2015-03, Vol.2015 (1), p.1-16, Article 97 |
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| container_title | Advances in difference equations |
| container_volume | 2015 |
| creator | Yang, Jiashan Qin, Xuewen |
| description | This paper is concerned with oscillations of certain second-order Emden-Fowler variable delay functional dynamic equations with damping and neutral of the form
[
A
(
t
)
φ
(
y
Δ
(
t
)
)
]
Δ
+
b
(
t
)
φ
(
y
Δ
(
t
)
)
+
P
(
t
)
F
(
φ
(
x
(
δ
(
t
)
)
)
)
−
Q
(
t
)
f
(
φ
(
x
(
γ
(
t
)
)
)
)
=
0
on an arbitrary time scale
T
, where
y
(
t
)
=
x
(
t
)
+
B
(
t
)
x
(
τ
(
t
)
)
and
φ
(
u
)
=
|
u
|
λ
−
1
u
(
λ
>
0
). By using the generalized Riccati transformation and the inequality technique, some new oscillation criteria for the equations are established. Our results extend and improve some known results, but they also unify the oscillation of second-order Emden-Fowler delay differential equations with damping and second-order Emden-Fowler delay difference equations with damping. Examples are given to illustrate the importance of our results. |
| doi_str_mv | 10.1186/s13662-014-0338-x |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1685809883</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3641930661</sourcerecordid><originalsourceid>FETCH-LOGICAL-c392t-c93112341dd4ad91fb3ef41b9981964a43bb59f2f30a79f0969576288c80f7f43</originalsourceid><addsrcrecordid>eNp1kU1LAzEQhhdRsFZ_gLeAFy_RZJNmk6MUv6DQi55Dmo-aspu0yS5t_72p9VAETzMDz_sOM29V3WL0gDFnjxkTxmqIMIWIEA53Z9UIM95AzGlzftJfVlc5rxCqBeV8VO3nWfu2Vb2PAejke5u8Ai4moG3qlQ8gWx2DgTEZm8BzZ2yAL3HblsHYVu2BG4I-qFULzD6ozmtgN8OPYQZb338Bo7q1D0tQNvS-syBr1dp8XV041WZ781vH1efL88f0Dc7mr-_TpxnURNQ91IJgXBOKjaHKCOwWxDqKF0JwLBhVlCwWE-FqR5BqhEOCiUnDas41R65xlIyr-6PvOsXNYHMvO5-1LTcHG4csy2cmHAnOSUHv_qCrOKRy2YFiHNUTxnGh8JHSKeacrJPr5DuV9hIjeQhDHsOQJQx5CEPuiqY-anJhw9KmE-d_Rd_rKI5U</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1668025681</pqid></control><display><type>article</type><title>Oscillation criteria for certain second-order Emden-Fowler delay functional dynamic equations with damping on time scales</title><source>DOAJ Directory of Open Access Journals</source><source>EZB-FREE-00999 freely available EZB journals</source><creator>Yang, Jiashan ; Qin, Xuewen</creator><creatorcontrib>Yang, Jiashan ; Qin, Xuewen</creatorcontrib><description>This paper is concerned with oscillations of certain second-order Emden-Fowler variable delay functional dynamic equations with damping and neutral of the form
[
A
(
t
)
φ
(
y
Δ
(
t
)
)
]
Δ
+
b
(
t
)
φ
(
y
Δ
(
t
)
)
+
P
(
t
)
F
(
φ
(
x
(
δ
(
t
)
)
)
)
−
Q
(
t
)
f
(
φ
(
x
(
γ
(
t
)
)
)
)
=
0
on an arbitrary time scale
T
, where
y
(
t
)
=
x
(
t
)
+
B
(
t
)
x
(
τ
(
t
)
)
and
φ
(
u
)
=
|
u
|
λ
−
1
u
(
λ
>
0
). By using the generalized Riccati transformation and the inequality technique, some new oscillation criteria for the equations are established. Our results extend and improve some known results, but they also unify the oscillation of second-order Emden-Fowler delay differential equations with damping and second-order Emden-Fowler delay difference equations with damping. Examples are given to illustrate the importance of our results.</description><identifier>ISSN: 1687-1847</identifier><identifier>ISSN: 1687-1839</identifier><identifier>EISSN: 1687-1847</identifier><identifier>DOI: 10.1186/s13662-014-0338-x</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Criteria ; Damping ; Delay ; Difference and Functional Equations ; Difference equations ; Dynamics ; Functional Analysis ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations ; Oscillations ; Partial Differential Equations ; Texts ; Time</subject><ispartof>Advances in difference equations, 2015-03, Vol.2015 (1), p.1-16, Article 97</ispartof><rights>Yang and Qin; licensee Springer 2015</rights><rights>The Author(s) 2015</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c392t-c93112341dd4ad91fb3ef41b9981964a43bb59f2f30a79f0969576288c80f7f43</citedby><cites>FETCH-LOGICAL-c392t-c93112341dd4ad91fb3ef41b9981964a43bb59f2f30a79f0969576288c80f7f43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,860,27901,27902</link.rule.ids></links><search><creatorcontrib>Yang, Jiashan</creatorcontrib><creatorcontrib>Qin, Xuewen</creatorcontrib><title>Oscillation criteria for certain second-order Emden-Fowler delay functional dynamic equations with damping on time scales</title><title>Advances in difference equations</title><addtitle>Adv Differ Equ</addtitle><description>This paper is concerned with oscillations of certain second-order Emden-Fowler variable delay functional dynamic equations with damping and neutral of the form
[
A
(
t
)
φ
(
y
Δ
(
t
)
)
]
Δ
+
b
(
t
)
φ
(
y
Δ
(
t
)
)
+
P
(
t
)
F
(
φ
(
x
(
δ
(
t
)
)
)
)
−
Q
(
t
)
f
(
φ
(
x
(
γ
(
t
)
)
)
)
=
0
on an arbitrary time scale
T
, where
y
(
t
)
=
x
(
t
)
+
B
(
t
)
x
(
τ
(
t
)
)
and
φ
(
u
)
=
|
u
|
λ
−
1
u
(
λ
>
0
). By using the generalized Riccati transformation and the inequality technique, some new oscillation criteria for the equations are established. Our results extend and improve some known results, but they also unify the oscillation of second-order Emden-Fowler delay differential equations with damping and second-order Emden-Fowler delay difference equations with damping. Examples are given to illustrate the importance of our results.</description><subject>Analysis</subject><subject>Criteria</subject><subject>Damping</subject><subject>Delay</subject><subject>Difference and Functional Equations</subject><subject>Difference equations</subject><subject>Dynamics</subject><subject>Functional Analysis</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><subject>Oscillations</subject><subject>Partial Differential Equations</subject><subject>Texts</subject><subject>Time</subject><issn>1687-1847</issn><issn>1687-1839</issn><issn>1687-1847</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>BENPR</sourceid><recordid>eNp1kU1LAzEQhhdRsFZ_gLeAFy_RZJNmk6MUv6DQi55Dmo-aspu0yS5t_72p9VAETzMDz_sOM29V3WL0gDFnjxkTxmqIMIWIEA53Z9UIM95AzGlzftJfVlc5rxCqBeV8VO3nWfu2Vb2PAejke5u8Ai4moG3qlQ8gWx2DgTEZm8BzZ2yAL3HblsHYVu2BG4I-qFULzD6ozmtgN8OPYQZb338Bo7q1D0tQNvS-syBr1dp8XV041WZ781vH1efL88f0Dc7mr-_TpxnURNQ91IJgXBOKjaHKCOwWxDqKF0JwLBhVlCwWE-FqR5BqhEOCiUnDas41R65xlIyr-6PvOsXNYHMvO5-1LTcHG4csy2cmHAnOSUHv_qCrOKRy2YFiHNUTxnGh8JHSKeacrJPr5DuV9hIjeQhDHsOQJQx5CEPuiqY-anJhw9KmE-d_Rd_rKI5U</recordid><startdate>20150326</startdate><enddate>20150326</enddate><creator>Yang, Jiashan</creator><creator>Qin, Xuewen</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20150326</creationdate><title>Oscillation criteria for certain second-order Emden-Fowler delay functional dynamic equations with damping on time scales</title><author>Yang, Jiashan ; Qin, Xuewen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c392t-c93112341dd4ad91fb3ef41b9981964a43bb59f2f30a79f0969576288c80f7f43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Analysis</topic><topic>Criteria</topic><topic>Damping</topic><topic>Delay</topic><topic>Difference and Functional Equations</topic><topic>Difference equations</topic><topic>Dynamics</topic><topic>Functional Analysis</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equations</topic><topic>Oscillations</topic><topic>Partial Differential Equations</topic><topic>Texts</topic><topic>Time</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yang, Jiashan</creatorcontrib><creatorcontrib>Qin, Xuewen</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Advances in difference equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yang, Jiashan</au><au>Qin, Xuewen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Oscillation criteria for certain second-order Emden-Fowler delay functional dynamic equations with damping on time scales</atitle><jtitle>Advances in difference equations</jtitle><stitle>Adv Differ Equ</stitle><date>2015-03-26</date><risdate>2015</risdate><volume>2015</volume><issue>1</issue><spage>1</spage><epage>16</epage><pages>1-16</pages><artnum>97</artnum><issn>1687-1847</issn><issn>1687-1839</issn><eissn>1687-1847</eissn><abstract>This paper is concerned with oscillations of certain second-order Emden-Fowler variable delay functional dynamic equations with damping and neutral of the form
[
A
(
t
)
φ
(
y
Δ
(
t
)
)
]
Δ
+
b
(
t
)
φ
(
y
Δ
(
t
)
)
+
P
(
t
)
F
(
φ
(
x
(
δ
(
t
)
)
)
)
−
Q
(
t
)
f
(
φ
(
x
(
γ
(
t
)
)
)
)
=
0
on an arbitrary time scale
T
, where
y
(
t
)
=
x
(
t
)
+
B
(
t
)
x
(
τ
(
t
)
)
and
φ
(
u
)
=
|
u
|
λ
−
1
u
(
λ
>
0
). By using the generalized Riccati transformation and the inequality technique, some new oscillation criteria for the equations are established. Our results extend and improve some known results, but they also unify the oscillation of second-order Emden-Fowler delay differential equations with damping and second-order Emden-Fowler delay difference equations with damping. Examples are given to illustrate the importance of our results.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1186/s13662-014-0338-x</doi><tpages>16</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1687-1847 |
| ispartof | Advances in difference equations, 2015-03, Vol.2015 (1), p.1-16, Article 97 |
| issn | 1687-1847 1687-1839 1687-1847 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1685809883 |
| source | DOAJ Directory of Open Access Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Analysis Criteria Damping Delay Difference and Functional Equations Difference equations Dynamics Functional Analysis Mathematical analysis Mathematics Mathematics and Statistics Ordinary Differential Equations Oscillations Partial Differential Equations Texts Time |
| title | Oscillation criteria for certain second-order Emden-Fowler delay functional dynamic equations with damping on time scales |
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