Liouville type theorems, a priori estimates and existence of solutions for sub-critical order Lane—Emden—Hardy equations
We study the sub-critical order Lane—Emden—Hardy equations (0.1) ( − Δ ) m u ( x ) = u p ( x ) | x | a in ℝ n with n ≥ 3, 1 ≤ m < n 2 , 0 ≤ a < 2 m and p > 1. We establish Liouville theorems in the ranges 1 < p < n + 2 m − 2 a n − 2 m if 0 ≤ a < 2 and 1 < p < +∞ if 2 ≤ a <...
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| Veröffentlicht in: | Journal d'analyse mathématique (Jerusalem) 2022, Vol.146 (2), p.673-718 |
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| container_title | Journal d'analyse mathématique (Jerusalem) |
| container_volume | 146 |
| creator | Dai, Wei Peng, Shaolong Qin, Guolin |
| description | We study the sub-critical order Lane—Emden—Hardy equations
(0.1)
(
−
Δ
)
m
u
(
x
)
=
u
p
(
x
)
|
x
|
a
in
ℝ
n
with
n
≥ 3,
1
≤
m
<
n
2
, 0 ≤
a
< 2
m
and
p
> 1. We establish Liouville theorems in the ranges
1
<
p
<
n
+
2
m
−
2
a
n
−
2
m
if 0 ≤
a
< 2 and 1 <
p
< +∞ if 2 ≤
a
< 2
m
for nonnegative classical solutions of equations (0.1), that is, the unique nonnegative solution is
u
≡ 0. As an application, we derive a priori estimates and the existence of positive solutions to sub-critical order Lane—Emden equations in bounded domains. |
| doi_str_mv | 10.1007/s11854-022-0207-6 |
| format | Article |
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(0.1)
(
−
Δ
)
m
u
(
x
)
=
u
p
(
x
)
|
x
|
a
in
ℝ
n
with
n
≥ 3,
1
≤
m
<
n
2
, 0 ≤
a
< 2
m
and
p
> 1. We establish Liouville theorems in the ranges
1
<
p
<
n
+
2
m
−
2
a
n
−
2
m
if 0 ≤
a
< 2 and 1 <
p
< +∞ if 2 ≤
a
< 2
m
for nonnegative classical solutions of equations (0.1), that is, the unique nonnegative solution is
u
≡ 0. As an application, we derive a priori estimates and the existence of positive solutions to sub-critical order Lane—Emden equations in bounded domains.]]></description><identifier>ISSN: 0021-7670</identifier><identifier>EISSN: 1565-8538</identifier><identifier>DOI: 10.1007/s11854-022-0207-6</identifier><language>eng</language><publisher>Jerusalem: The Hebrew University Magnes Press</publisher><subject>Abstract Harmonic Analysis ; Analysis ; Dynamical Systems and Ergodic Theory ; Estimates ; Existence theorems ; Functional Analysis ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Partial Differential Equations</subject><ispartof>Journal d'analyse mathématique (Jerusalem), 2022, Vol.146 (2), p.673-718</ispartof><rights>The Hebrew University of Jerusalem 2022</rights><rights>The Hebrew University of Jerusalem 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c246t-60e0244cf94d47b891d63af4fe187a90133d44b1d52a2f88d4d33249517351d63</citedby><cites>FETCH-LOGICAL-c246t-60e0244cf94d47b891d63af4fe187a90133d44b1d52a2f88d4d33249517351d63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11854-022-0207-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11854-022-0207-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Dai, Wei</creatorcontrib><creatorcontrib>Peng, Shaolong</creatorcontrib><creatorcontrib>Qin, Guolin</creatorcontrib><title>Liouville type theorems, a priori estimates and existence of solutions for sub-critical order Lane—Emden—Hardy equations</title><title>Journal d'analyse mathématique (Jerusalem)</title><addtitle>JAMA</addtitle><description><![CDATA[We study the sub-critical order Lane—Emden—Hardy equations
(0.1)
(
−
Δ
)
m
u
(
x
)
=
u
p
(
x
)
|
x
|
a
in
ℝ
n
with
n
≥ 3,
1
≤
m
<
n
2
, 0 ≤
a
< 2
m
and
p
> 1. We establish Liouville theorems in the ranges
1
<
p
<
n
+
2
m
−
2
a
n
−
2
m
if 0 ≤
a
< 2 and 1 <
p
< +∞ if 2 ≤
a
< 2
m
for nonnegative classical solutions of equations (0.1), that is, the unique nonnegative solution is
u
≡ 0. As an application, we derive a priori estimates and the existence of positive solutions to sub-critical order Lane—Emden equations in bounded domains.]]></description><subject>Abstract Harmonic Analysis</subject><subject>Analysis</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Estimates</subject><subject>Existence theorems</subject><subject>Functional Analysis</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial Differential Equations</subject><issn>0021-7670</issn><issn>1565-8538</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp1kE1OwzAQhS0EEqVwAHaW2BIYO3Z-lqgqFKkSG1hbbjwBV0nc2gmiEgsOwQk5CQ5FYsVi5m3ee6P5CDlncMUA8uvAWCFFApzHgTzJDsiEyUwmhUyLQzIB4CzJsxyOyUkIawApy5RPyPvSuuHVNg3SfreJ6wWdxzZcUk033jpvKYbetrrHQHVnKL7Z0GNXIXU1Da4Zeuu6QGvnaRhWSeVtbyvdUOcNerrUHX59fM5bg13UhfZmR3E76J_UKTmqdRPw7Fen5Ol2_jhbJMuHu_vZzTKpuMj6JAMELkRVl8KIfFWUzGSprkWNrMh1CSxNjRArZiTXvC4KI0yaclFKlqdy9E7Jxb534912iP-otRt8F08qngOTkhcA0cX2rsq7EDzWKgJotd8pBmqErPaQVYSsRshqbOb7TIje7hn9X_P_oW9fMoIX</recordid><startdate>2022</startdate><enddate>2022</enddate><creator>Dai, Wei</creator><creator>Peng, Shaolong</creator><creator>Qin, Guolin</creator><general>The Hebrew University Magnes Press</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>2022</creationdate><title>Liouville type theorems, a priori estimates and existence of solutions for sub-critical order Lane—Emden—Hardy equations</title><author>Dai, Wei ; Peng, Shaolong ; Qin, Guolin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c246t-60e0244cf94d47b891d63af4fe187a90133d44b1d52a2f88d4d33249517351d63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Analysis</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Estimates</topic><topic>Existence theorems</topic><topic>Functional Analysis</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial Differential Equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dai, Wei</creatorcontrib><creatorcontrib>Peng, Shaolong</creatorcontrib><creatorcontrib>Qin, Guolin</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal d'analyse mathématique (Jerusalem)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dai, Wei</au><au>Peng, Shaolong</au><au>Qin, Guolin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Liouville type theorems, a priori estimates and existence of solutions for sub-critical order Lane—Emden—Hardy equations</atitle><jtitle>Journal d'analyse mathématique (Jerusalem)</jtitle><stitle>JAMA</stitle><date>2022</date><risdate>2022</risdate><volume>146</volume><issue>2</issue><spage>673</spage><epage>718</epage><pages>673-718</pages><issn>0021-7670</issn><eissn>1565-8538</eissn><abstract><![CDATA[We study the sub-critical order Lane—Emden—Hardy equations
(0.1)
(
−
Δ
)
m
u
(
x
)
=
u
p
(
x
)
|
x
|
a
in
ℝ
n
with
n
≥ 3,
1
≤
m
<
n
2
, 0 ≤
a
< 2
m
and
p
> 1. We establish Liouville theorems in the ranges
1
<
p
<
n
+
2
m
−
2
a
n
−
2
m
if 0 ≤
a
< 2 and 1 <
p
< +∞ if 2 ≤
a
< 2
m
for nonnegative classical solutions of equations (0.1), that is, the unique nonnegative solution is
u
≡ 0. As an application, we derive a priori estimates and the existence of positive solutions to sub-critical order Lane—Emden equations in bounded domains.]]></abstract><cop>Jerusalem</cop><pub>The Hebrew University Magnes Press</pub><doi>10.1007/s11854-022-0207-6</doi><tpages>46</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-7670 |
| ispartof | Journal d'analyse mathématique (Jerusalem), 2022, Vol.146 (2), p.673-718 |
| issn | 0021-7670 1565-8538 |
| language | eng |
| recordid | cdi_proquest_journals_2701552800 |
| source | SpringerLink Journals |
| subjects | Abstract Harmonic Analysis Analysis Dynamical Systems and Ergodic Theory Estimates Existence theorems Functional Analysis Mathematical analysis Mathematics Mathematics and Statistics Partial Differential Equations |
| title | Liouville type theorems, a priori estimates and existence of solutions for sub-critical order Lane—Emden—Hardy equations |
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