First and second critical exponents for an inhomogeneous Schrödinger equation with combined nonlinearities
We study the large-time behavior of solutions for the inhomogeneous nonlinear Schrödinger equation i u t + Δ u = λ | u | p + μ | ∇ u | q + w ( x ) , t > 0 , x ∈ R N , where N ≥ 1 , p , q > 1 , λ , μ ∈ C , λ ≠ 0 , and u ( 0 , · ) , w ∈ L loc 1 ( R N , C ) . We consider both the cases where μ =...
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| Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Physik 2022-08, Vol.73 (4), Article 157 |
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| container_title | Zeitschrift für angewandte Mathematik und Physik |
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| creator | Alotaibi, Munirah Jleli, Mohamed Samet, Bessem Vetro, Calogero |
| description | We study the large-time behavior of solutions for the inhomogeneous nonlinear Schrödinger equation
i
u
t
+
Δ
u
=
λ
|
u
|
p
+
μ
|
∇
u
|
q
+
w
(
x
)
,
t
>
0
,
x
∈
R
N
,
where
N
≥
1
,
p
,
q
>
1
,
λ
,
μ
∈
C
,
λ
≠
0
, and
u
(
0
,
·
)
,
w
∈
L
loc
1
(
R
N
,
C
)
. We consider both the cases where
μ
=
0
and
μ
≠
0
, respectively. We establish existence/nonexistence of global weak solutions. In each studied case, we compute the critical exponents in the sense of Fujita, and Lee and Ni. When
μ
≠
0
, we show that the nonlinearity
|
∇
u
|
q
induces an interesting phenomenon of discontinuity of the Fujita critical exponent. |
| doi_str_mv | 10.1007/s00033-022-01784-y |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2684589537</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2684589537</sourcerecordid><originalsourceid>FETCH-LOGICAL-c363t-5896cb9798ee4755a90b731b89dda977e5e29ff97863ae451204720628e2201c3</originalsourceid><addsrcrecordid>eNp9kMFKAzEQhoMoWKsv4CngeXWS7G42RylWhYIH9RzS7Gyb2iZtskX7Yr6AL2ZqBW-eZg7f_w3zE3LJ4JoByJsEAEIUwHkBTDZlsTsiA1ZyKBQIdUwGAGVZcC6rU3KW0iLjkoEYkLexi6mnxrc0oQ152Oh6Z82S4sc6ePR9ol2ImaDOz8MqzNBj2Cb6bOfx67N1foaR4mZrehc8fXf9nNqwmjqPLfXBL_Ni9kpM5-SkM8uEF79zSF7Hdy-jh2LydP84up0UVtSiL6pG1XaqpGoQS1lVRsFUCjZtVNsaJSVWyFXXKdnUwmBZMQ6l5FDzBjkHZsWQXB286xg2W0y9XoRt9Pmk5nVTZn8lZKb4gbIxpBSx0-voVibuNAO9L1UfStW5VP1Tqt7lkDiEUob3n_-p_0l9A5PSfIE</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2684589537</pqid></control><display><type>article</type><title>First and second critical exponents for an inhomogeneous Schrödinger equation with combined nonlinearities</title><source>SpringerNature Journals</source><creator>Alotaibi, Munirah ; Jleli, Mohamed ; Samet, Bessem ; Vetro, Calogero</creator><creatorcontrib>Alotaibi, Munirah ; Jleli, Mohamed ; Samet, Bessem ; Vetro, Calogero</creatorcontrib><description>We study the large-time behavior of solutions for the inhomogeneous nonlinear Schrödinger equation
i
u
t
+
Δ
u
=
λ
|
u
|
p
+
μ
|
∇
u
|
q
+
w
(
x
)
,
t
>
0
,
x
∈
R
N
,
where
N
≥
1
,
p
,
q
>
1
,
λ
,
μ
∈
C
,
λ
≠
0
, and
u
(
0
,
·
)
,
w
∈
L
loc
1
(
R
N
,
C
)
. We consider both the cases where
μ
=
0
and
μ
≠
0
, respectively. We establish existence/nonexistence of global weak solutions. In each studied case, we compute the critical exponents in the sense of Fujita, and Lee and Ni. When
μ
≠
0
, we show that the nonlinearity
|
∇
u
|
q
induces an interesting phenomenon of discontinuity of the Fujita critical exponent.</description><identifier>ISSN: 0044-2275</identifier><identifier>EISSN: 1420-9039</identifier><identifier>DOI: 10.1007/s00033-022-01784-y</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Engineering ; Exponents ; Mathematical Methods in Physics ; Nonlinearity ; Schrodinger equation ; Theoretical and Applied Mechanics</subject><ispartof>Zeitschrift für angewandte Mathematik und Physik, 2022-08, Vol.73 (4), Article 157</ispartof><rights>The Author(s) 2022</rights><rights>The Author(s) 2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-5896cb9798ee4755a90b731b89dda977e5e29ff97863ae451204720628e2201c3</citedby><cites>FETCH-LOGICAL-c363t-5896cb9798ee4755a90b731b89dda977e5e29ff97863ae451204720628e2201c3</cites><orcidid>0000-0001-5836-6847</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00033-022-01784-y$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00033-022-01784-y$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Alotaibi, Munirah</creatorcontrib><creatorcontrib>Jleli, Mohamed</creatorcontrib><creatorcontrib>Samet, Bessem</creatorcontrib><creatorcontrib>Vetro, Calogero</creatorcontrib><title>First and second critical exponents for an inhomogeneous Schrödinger equation with combined nonlinearities</title><title>Zeitschrift für angewandte Mathematik und Physik</title><addtitle>Z. Angew. Math. Phys</addtitle><description>We study the large-time behavior of solutions for the inhomogeneous nonlinear Schrödinger equation
i
u
t
+
Δ
u
=
λ
|
u
|
p
+
μ
|
∇
u
|
q
+
w
(
x
)
,
t
>
0
,
x
∈
R
N
,
where
N
≥
1
,
p
,
q
>
1
,
λ
,
μ
∈
C
,
λ
≠
0
, and
u
(
0
,
·
)
,
w
∈
L
loc
1
(
R
N
,
C
)
. We consider both the cases where
μ
=
0
and
μ
≠
0
, respectively. We establish existence/nonexistence of global weak solutions. In each studied case, we compute the critical exponents in the sense of Fujita, and Lee and Ni. When
μ
≠
0
, we show that the nonlinearity
|
∇
u
|
q
induces an interesting phenomenon of discontinuity of the Fujita critical exponent.</description><subject>Engineering</subject><subject>Exponents</subject><subject>Mathematical Methods in Physics</subject><subject>Nonlinearity</subject><subject>Schrodinger equation</subject><subject>Theoretical and Applied Mechanics</subject><issn>0044-2275</issn><issn>1420-9039</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kMFKAzEQhoMoWKsv4CngeXWS7G42RylWhYIH9RzS7Gyb2iZtskX7Yr6AL2ZqBW-eZg7f_w3zE3LJ4JoByJsEAEIUwHkBTDZlsTsiA1ZyKBQIdUwGAGVZcC6rU3KW0iLjkoEYkLexi6mnxrc0oQ152Oh6Z82S4sc6ePR9ol2ImaDOz8MqzNBj2Cb6bOfx67N1foaR4mZrehc8fXf9nNqwmjqPLfXBL_Ni9kpM5-SkM8uEF79zSF7Hdy-jh2LydP84up0UVtSiL6pG1XaqpGoQS1lVRsFUCjZtVNsaJSVWyFXXKdnUwmBZMQ6l5FDzBjkHZsWQXB286xg2W0y9XoRt9Pmk5nVTZn8lZKb4gbIxpBSx0-voVibuNAO9L1UfStW5VP1Tqt7lkDiEUob3n_-p_0l9A5PSfIE</recordid><startdate>20220801</startdate><enddate>20220801</enddate><creator>Alotaibi, Munirah</creator><creator>Jleli, Mohamed</creator><creator>Samet, Bessem</creator><creator>Vetro, Calogero</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-5836-6847</orcidid></search><sort><creationdate>20220801</creationdate><title>First and second critical exponents for an inhomogeneous Schrödinger equation with combined nonlinearities</title><author>Alotaibi, Munirah ; Jleli, Mohamed ; Samet, Bessem ; Vetro, Calogero</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-5896cb9798ee4755a90b731b89dda977e5e29ff97863ae451204720628e2201c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Engineering</topic><topic>Exponents</topic><topic>Mathematical Methods in Physics</topic><topic>Nonlinearity</topic><topic>Schrodinger equation</topic><topic>Theoretical and Applied Mechanics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Alotaibi, Munirah</creatorcontrib><creatorcontrib>Jleli, Mohamed</creatorcontrib><creatorcontrib>Samet, Bessem</creatorcontrib><creatorcontrib>Vetro, Calogero</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Alotaibi, Munirah</au><au>Jleli, Mohamed</au><au>Samet, Bessem</au><au>Vetro, Calogero</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>First and second critical exponents for an inhomogeneous Schrödinger equation with combined nonlinearities</atitle><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle><stitle>Z. Angew. Math. Phys</stitle><date>2022-08-01</date><risdate>2022</risdate><volume>73</volume><issue>4</issue><artnum>157</artnum><issn>0044-2275</issn><eissn>1420-9039</eissn><abstract>We study the large-time behavior of solutions for the inhomogeneous nonlinear Schrödinger equation
i
u
t
+
Δ
u
=
λ
|
u
|
p
+
μ
|
∇
u
|
q
+
w
(
x
)
,
t
>
0
,
x
∈
R
N
,
where
N
≥
1
,
p
,
q
>
1
,
λ
,
μ
∈
C
,
λ
≠
0
, and
u
(
0
,
·
)
,
w
∈
L
loc
1
(
R
N
,
C
)
. We consider both the cases where
μ
=
0
and
μ
≠
0
, respectively. We establish existence/nonexistence of global weak solutions. In each studied case, we compute the critical exponents in the sense of Fujita, and Lee and Ni. When
μ
≠
0
, we show that the nonlinearity
|
∇
u
|
q
induces an interesting phenomenon of discontinuity of the Fujita critical exponent.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00033-022-01784-y</doi><orcidid>https://orcid.org/0000-0001-5836-6847</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0044-2275 |
| ispartof | Zeitschrift für angewandte Mathematik und Physik, 2022-08, Vol.73 (4), Article 157 |
| issn | 0044-2275 1420-9039 |
| language | eng |
| recordid | cdi_proquest_journals_2684589537 |
| source | SpringerNature Journals |
| subjects | Engineering Exponents Mathematical Methods in Physics Nonlinearity Schrodinger equation Theoretical and Applied Mechanics |
| title | First and second critical exponents for an inhomogeneous Schrödinger equation with combined nonlinearities |
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