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Existence of positive radial solutions for nonlinear elliptic equations with gradient terms in an annulus
In this paper, we concern with the existence of positive radial solutions of the elliptic equation with nonlinear gradient term - Δ u = f ( | u | , u , x | x | · ∇ u ) , x ∈ Ω , u | ∂ Ω = 0 , where Ω = { x ∈ R n : a < | x | < b } , 0 < a < b < ∞ , n ≥ 3 , f ∈ [ a , b ] × R + × R → R +...
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| Published in: | Journal of elliptic and parabolic equations 2023-12, Vol.9 (2), p.807-829 |
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| Format: | Article |
| Language: | English |
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| container_end_page | 829 |
| container_issue | 2 |
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| container_title | Journal of elliptic and parabolic equations |
| container_volume | 9 |
| creator | Gou, Haide |
| description | In this paper, we concern with the existence of positive radial solutions of the elliptic equation with nonlinear gradient term
-
Δ
u
=
f
(
|
u
|
,
u
,
x
|
x
|
·
∇
u
)
,
x
∈
Ω
,
u
|
∂
Ω
=
0
,
where
Ω
=
{
x
∈
R
n
:
a
<
|
x
|
<
b
}
,
0
<
a
<
b
<
∞
,
n
≥
3
,
f
∈
[
a
,
b
]
×
R
+
×
R
→
R
+
is continuous. Under the conditions that the nonlinearity
f
(
r
,
u
,
η
)
may be of superlinear or sublinear growth in
u
and
η
, existence results of positive radial solutions are obtained. For the superlinear case, the growth of
f
in
η
is restricted to quadratic growth. The superlinear and the sublinear growth of the nonlinearity of
f
are described by inequality conditions instead of the usual upper and lower limits conditions as well as the nonlinearity is related to derivative terms. The result is obtained basing on the fixed point index theory in cones. |
| doi_str_mv | 10.1007/s41808-023-00224-w |
| format | article |
| fullrecord | <record><control><sourceid>crossref_sprin</sourceid><recordid>TN_cdi_crossref_primary_10_1007_s41808_023_00224_w</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1007_s41808_023_00224_w</sourcerecordid><originalsourceid>FETCH-LOGICAL-c242t-c20382249712b49ecce96dfd34ba4d283d947e74a56f9616c0a7a6c2c27e2dd93</originalsourceid><addsrcrecordid>eNp9kM9OAyEQh4nRxEb7Ap54gVUWEJajaeqfpIkXPRPKzlYaChVYq28vdY1HEzLM4fdNZj6Erlpy3RIibzJvO9I1hLKGEEp5czhBM0qVaBRh6vSvp-QczXPekpqSjEtBZsgtP10uECzgOOB9zK64D8DJ9M54nKMfi4sh4yEmHGLwLoBJGLx3--IshvfRTIGDK294c-QgFFwg7TJ2AZvjC6Mf8yU6G4zPMP_9L9Dr_fJl8disnh-eFnerxlJOS62EdfUIJVu65gqsBSX6oWd8bXhPO9YrLkFycysGJVphiZFGWGqpBNr3il0gOs21KeacYND75HYmfemW6KMvPfnS1Zf-8aUPFWITlGs4bCDpbRxTqHv-R30Dftlw4A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Existence of positive radial solutions for nonlinear elliptic equations with gradient terms in an annulus</title><source>Springer Link</source><creator>Gou, Haide</creator><creatorcontrib>Gou, Haide</creatorcontrib><description>In this paper, we concern with the existence of positive radial solutions of the elliptic equation with nonlinear gradient term
-
Δ
u
=
f
(
|
u
|
,
u
,
x
|
x
|
·
∇
u
)
,
x
∈
Ω
,
u
|
∂
Ω
=
0
,
where
Ω
=
{
x
∈
R
n
:
a
<
|
x
|
<
b
}
,
0
<
a
<
b
<
∞
,
n
≥
3
,
f
∈
[
a
,
b
]
×
R
+
×
R
→
R
+
is continuous. Under the conditions that the nonlinearity
f
(
r
,
u
,
η
)
may be of superlinear or sublinear growth in
u
and
η
, existence results of positive radial solutions are obtained. For the superlinear case, the growth of
f
in
η
is restricted to quadratic growth. The superlinear and the sublinear growth of the nonlinearity of
f
are described by inequality conditions instead of the usual upper and lower limits conditions as well as the nonlinearity is related to derivative terms. The result is obtained basing on the fixed point index theory in cones.</description><identifier>ISSN: 2296-9020</identifier><identifier>EISSN: 2296-9039</identifier><identifier>DOI: 10.1007/s41808-023-00224-w</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Mathematics ; Mathematics and Statistics ; Partial Differential Equations</subject><ispartof>Journal of elliptic and parabolic equations, 2023-12, Vol.9 (2), p.807-829</ispartof><rights>Orthogonal Publisher and Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c242t-c20382249712b49ecce96dfd34ba4d283d947e74a56f9616c0a7a6c2c27e2dd93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Gou, Haide</creatorcontrib><title>Existence of positive radial solutions for nonlinear elliptic equations with gradient terms in an annulus</title><title>Journal of elliptic and parabolic equations</title><addtitle>J Elliptic Parabol Equ</addtitle><description>In this paper, we concern with the existence of positive radial solutions of the elliptic equation with nonlinear gradient term
-
Δ
u
=
f
(
|
u
|
,
u
,
x
|
x
|
·
∇
u
)
,
x
∈
Ω
,
u
|
∂
Ω
=
0
,
where
Ω
=
{
x
∈
R
n
:
a
<
|
x
|
<
b
}
,
0
<
a
<
b
<
∞
,
n
≥
3
,
f
∈
[
a
,
b
]
×
R
+
×
R
→
R
+
is continuous. Under the conditions that the nonlinearity
f
(
r
,
u
,
η
)
may be of superlinear or sublinear growth in
u
and
η
, existence results of positive radial solutions are obtained. For the superlinear case, the growth of
f
in
η
is restricted to quadratic growth. The superlinear and the sublinear growth of the nonlinearity of
f
are described by inequality conditions instead of the usual upper and lower limits conditions as well as the nonlinearity is related to derivative terms. The result is obtained basing on the fixed point index theory in cones.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial Differential Equations</subject><issn>2296-9020</issn><issn>2296-9039</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kM9OAyEQh4nRxEb7Ap54gVUWEJajaeqfpIkXPRPKzlYaChVYq28vdY1HEzLM4fdNZj6Erlpy3RIibzJvO9I1hLKGEEp5czhBM0qVaBRh6vSvp-QczXPekpqSjEtBZsgtP10uECzgOOB9zK64D8DJ9M54nKMfi4sh4yEmHGLwLoBJGLx3--IshvfRTIGDK294c-QgFFwg7TJ2AZvjC6Mf8yU6G4zPMP_9L9Dr_fJl8disnh-eFnerxlJOS62EdfUIJVu65gqsBSX6oWd8bXhPO9YrLkFycysGJVphiZFGWGqpBNr3il0gOs21KeacYND75HYmfemW6KMvPfnS1Zf-8aUPFWITlGs4bCDpbRxTqHv-R30Dftlw4A</recordid><startdate>20231201</startdate><enddate>20231201</enddate><creator>Gou, Haide</creator><general>Springer International Publishing</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20231201</creationdate><title>Existence of positive radial solutions for nonlinear elliptic equations with gradient terms in an annulus</title><author>Gou, Haide</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c242t-c20382249712b49ecce96dfd34ba4d283d947e74a56f9616c0a7a6c2c27e2dd93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial Differential Equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gou, Haide</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of elliptic and parabolic equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gou, Haide</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence of positive radial solutions for nonlinear elliptic equations with gradient terms in an annulus</atitle><jtitle>Journal of elliptic and parabolic equations</jtitle><stitle>J Elliptic Parabol Equ</stitle><date>2023-12-01</date><risdate>2023</risdate><volume>9</volume><issue>2</issue><spage>807</spage><epage>829</epage><pages>807-829</pages><issn>2296-9020</issn><eissn>2296-9039</eissn><abstract>In this paper, we concern with the existence of positive radial solutions of the elliptic equation with nonlinear gradient term
-
Δ
u
=
f
(
|
u
|
,
u
,
x
|
x
|
·
∇
u
)
,
x
∈
Ω
,
u
|
∂
Ω
=
0
,
where
Ω
=
{
x
∈
R
n
:
a
<
|
x
|
<
b
}
,
0
<
a
<
b
<
∞
,
n
≥
3
,
f
∈
[
a
,
b
]
×
R
+
×
R
→
R
+
is continuous. Under the conditions that the nonlinearity
f
(
r
,
u
,
η
)
may be of superlinear or sublinear growth in
u
and
η
, existence results of positive radial solutions are obtained. For the superlinear case, the growth of
f
in
η
is restricted to quadratic growth. The superlinear and the sublinear growth of the nonlinearity of
f
are described by inequality conditions instead of the usual upper and lower limits conditions as well as the nonlinearity is related to derivative terms. The result is obtained basing on the fixed point index theory in cones.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s41808-023-00224-w</doi><tpages>23</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 2296-9020 |
| ispartof | Journal of elliptic and parabolic equations, 2023-12, Vol.9 (2), p.807-829 |
| issn | 2296-9020 2296-9039 |
| language | eng |
| recordid | cdi_crossref_primary_10_1007_s41808_023_00224_w |
| source | Springer Link |
| subjects | Mathematics Mathematics and Statistics Partial Differential Equations |
| title | Existence of positive radial solutions for nonlinear elliptic equations with gradient terms in an annulus |
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