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Exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems
We study the exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems { − [ φ ( u ′ ) ] ′ = λ u p ( 1 − u N ) in ( − L , L ) , u ( − L ) = u ( L ) = 0 , where p > 1, N > 0, λ > 0 is a bifurcation parameter, L > 0 is an evolution parameter, and ϕ (...
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| Published in: | Czechoslovak mathematical journal 2023-12, Vol.73 (4), p.1081-1098 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| container_end_page | 1098 |
| container_issue | 4 |
| container_start_page | 1081 |
| container_title | Czechoslovak mathematical journal |
| container_volume | 73 |
| creator | Huang, Shao-Yuan Hsieh, Ping-Han |
| description | We study the exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems
{
−
[
φ
(
u
′
)
]
′
=
λ
u
p
(
1
−
u
N
)
in
(
−
L
,
L
)
,
u
(
−
L
)
=
u
(
L
)
=
0
,
where
p
> 1,
N
> 0, λ > 0 is a bifurcation parameter,
L
> 0 is an evolution parameter, and
ϕ
(
u
) is either
ϕ
(
u
) =
u
or
φ
(
u
)
=
u
/
1
−
u
2
. We prove that the corresponding bifurcation curve is ⊂-shape. Thus, the exact multiplicity of positive solutions can be obtained. |
| doi_str_mv | 10.21136/CMJ.2023.0359-22 |
| format | article |
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{
−
[
φ
(
u
′
)
]
′
=
λ
u
p
(
1
−
u
N
)
in
(
−
L
,
L
)
,
u
(
−
L
)
=
u
(
L
)
=
0
,
where
p
> 1,
N
> 0, λ > 0 is a bifurcation parameter,
L
> 0 is an evolution parameter, and
ϕ
(
u
) is either
ϕ
(
u
) =
u
or
φ
(
u
)
=
u
/
1
−
u
2
. We prove that the corresponding bifurcation curve is ⊂-shape. Thus, the exact multiplicity of positive solutions can be obtained.</description><identifier>ISSN: 0011-4642</identifier><identifier>EISSN: 1572-9141</identifier><identifier>DOI: 10.21136/CMJ.2023.0359-22</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Bifurcations ; Convex and Discrete Geometry ; Mathematical Modeling and Industrial Mathematics ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations ; Parameters</subject><ispartof>Czechoslovak mathematical journal, 2023-12, Vol.73 (4), p.1081-1098</ispartof><rights>Institute of Mathematics, Czech Academy of Sciences 2023</rights><rights>Institute of Mathematics, Czech Academy of Sciences 2023.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c231t-3af641e4fe08e3445ebe58d8d73a266867df164e19eeaa1c5a2e917c8c1f07363</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Huang, Shao-Yuan</creatorcontrib><creatorcontrib>Hsieh, Ping-Han</creatorcontrib><title>Exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems</title><title>Czechoslovak mathematical journal</title><addtitle>Czech Math J</addtitle><description>We study the exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems
{
−
[
φ
(
u
′
)
]
′
=
λ
u
p
(
1
−
u
N
)
in
(
−
L
,
L
)
,
u
(
−
L
)
=
u
(
L
)
=
0
,
where
p
> 1,
N
> 0, λ > 0 is a bifurcation parameter,
L
> 0 is an evolution parameter, and
ϕ
(
u
) is either
ϕ
(
u
) =
u
or
φ
(
u
)
=
u
/
1
−
u
2
. We prove that the corresponding bifurcation curve is ⊂-shape. Thus, the exact multiplicity of positive solutions can be obtained.</description><subject>Analysis</subject><subject>Bifurcations</subject><subject>Convex and Discrete Geometry</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><subject>Parameters</subject><issn>0011-4642</issn><issn>1572-9141</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkF1LwzAUhoMoOKc_wLuA1505J2maXsqYX0y80euapacjo2trkw7119ttglcvnPfhvPAwdg1ihgBS385fnmcoUM6ETPME8YRNIM0wyUHBKZsIAZAorfCcXYSwEUJIUGbCPhZf1kW-Herou9o7H7-5bUq-8tXQOxt923A39DsKvK141wYf_Y54aOth3x2ua2qot7X_oZLX7dqH6B3v-nZV0zZcsrPK1oGu_nLK3u8Xb_PHZPn68DS_WyYOJcRE2korIFWRMCSVSmlFqSlNmUmLWhudlRVoRZATWQsutUg5ZM44qEQmtZyym-PfcfhzoBCLTTv0zThZoMlTCSjSfKTwSIWu982a-n8KRHEwWYwmi73JYm-yQJS_MaBogQ</recordid><startdate>20231201</startdate><enddate>20231201</enddate><creator>Huang, Shao-Yuan</creator><creator>Hsieh, Ping-Han</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>20231201</creationdate><title>Exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems</title><author>Huang, Shao-Yuan ; Hsieh, Ping-Han</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c231t-3af641e4fe08e3445ebe58d8d73a266867df164e19eeaa1c5a2e917c8c1f07363</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Analysis</topic><topic>Bifurcations</topic><topic>Convex and Discrete Geometry</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equations</topic><topic>Parameters</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Huang, Shao-Yuan</creatorcontrib><creatorcontrib>Hsieh, Ping-Han</creatorcontrib><jtitle>Czechoslovak mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Huang, Shao-Yuan</au><au>Hsieh, Ping-Han</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems</atitle><jtitle>Czechoslovak mathematical journal</jtitle><stitle>Czech Math J</stitle><date>2023-12-01</date><risdate>2023</risdate><volume>73</volume><issue>4</issue><spage>1081</spage><epage>1098</epage><pages>1081-1098</pages><issn>0011-4642</issn><eissn>1572-9141</eissn><abstract>We study the exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems
{
−
[
φ
(
u
′
)
]
′
=
λ
u
p
(
1
−
u
N
)
in
(
−
L
,
L
)
,
u
(
−
L
)
=
u
(
L
)
=
0
,
where
p
> 1,
N
> 0, λ > 0 is a bifurcation parameter,
L
> 0 is an evolution parameter, and
ϕ
(
u
) is either
ϕ
(
u
) =
u
or
φ
(
u
)
=
u
/
1
−
u
2
. We prove that the corresponding bifurcation curve is ⊂-shape. Thus, the exact multiplicity of positive solutions can be obtained.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.21136/CMJ.2023.0359-22</doi><tpages>18</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0011-4642 |
| ispartof | Czechoslovak mathematical journal, 2023-12, Vol.73 (4), p.1081-1098 |
| issn | 0011-4642 1572-9141 |
| language | eng |
| recordid | cdi_proquest_journals_2895312059 |
| source | Springer Nature |
| subjects | Analysis Bifurcations Convex and Discrete Geometry Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Ordinary Differential Equations Parameters |
| title | Exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems |
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