Existence and multiplicity results for a class of non-linear Schr\"odinger equations with magnetic potential involving sign-changing non linearity
In this work we consider the following class of elliptic problems $$- \Delta_A u + u = a(x) |u|^{q-2}u+b(x) |u|^{p-2}u , \mbox{ in } \mathbb{R}^N, $$ $u\in H^1_A (\mathbb{R}^N)$, with $2
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| creator | de Paiva, Francisco Odair Vieira Lima, Sandra Machado de Souza Miyagaki, Olimpio Hiroshi |
| description | In this work we consider the following class of elliptic problems $$-
\Delta_A u + u = a(x) |u|^{q-2}u+b(x) |u|^{p-2}u , \mbox{ in } \mathbb{R}^N, $$
$u\in H^1_A (\mathbb{R}^N)$, with $2 |
| doi_str_mv | 10.48550/arxiv.1904.06382 |
| format | Article |
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\Delta_A u + u = a(x) |u|^{q-2}u+b(x) |u|^{p-2}u , \mbox{ in } \mathbb{R}^N, $$
$u\in H^1_A (\mathbb{R}^N)$, with $2<q<p<2^*= \frac{2N}{N-2}$, $a(x)$ and
$b(x)$ are functions that can change signal and satisfy some additional
conditions; $u \in H^1_A(\mathbb{R}^N)$ and $A:\mathbb{R}^N \rightarrow
\mathbb{R}^N$ is a magnetic potential. Also using the Nehari method in
combination with other complementary arguments, we discuss the existence of
infinite solutions to the problem in question, varying the assumptions about
the weight functions.</description><identifier>DOI: 10.48550/arxiv.1904.06382</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2019-04</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1904.06382$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1904.06382$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>de Paiva, Francisco Odair Vieira</creatorcontrib><creatorcontrib>Lima, Sandra Machado de Souza</creatorcontrib><creatorcontrib>Miyagaki, Olimpio Hiroshi</creatorcontrib><title>Existence and multiplicity results for a class of non-linear Schr\"odinger equations with magnetic potential involving sign-changing non linearity</title><description>In this work we consider the following class of elliptic problems $$-
\Delta_A u + u = a(x) |u|^{q-2}u+b(x) |u|^{p-2}u , \mbox{ in } \mathbb{R}^N, $$
$u\in H^1_A (\mathbb{R}^N)$, with $2<q<p<2^*= \frac{2N}{N-2}$, $a(x)$ and
$b(x)$ are functions that can change signal and satisfy some additional
conditions; $u \in H^1_A(\mathbb{R}^N)$ and $A:\mathbb{R}^N \rightarrow
\mathbb{R}^N$ is a magnetic potential. Also using the Nehari method in
combination with other complementary arguments, we discuss the existence of
infinite solutions to the problem in question, varying the assumptions about
the weight functions.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNqFjzsOwjAQRN1QIOAAVKzoE8InKNQIRA8lUrRynGQlZx1sE-AanBjz6alGI43ezAgxnifxKkvTZIb2Tl083ySrOFkvs0VfPHd3cl6xVIBcQHPVnlpNkvwDrHLBOiiNBQSp0TkwJbDhSBMrtHCUtT1PTUFcKQvqckVPhh3cyNfQYMXKk4TWhAJPqIG4M7oLaXBUcSRr5OrtAhK-yNA7FL0StVOjnw7EZL87bQ_RZ33eWmrQPvL3i_zzYvk_8QJ-hVad</recordid><startdate>20190412</startdate><enddate>20190412</enddate><creator>de Paiva, Francisco Odair Vieira</creator><creator>Lima, Sandra Machado de Souza</creator><creator>Miyagaki, Olimpio Hiroshi</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20190412</creationdate><title>Existence and multiplicity results for a class of non-linear Schr\"odinger equations with magnetic potential involving sign-changing non linearity</title><author>de Paiva, Francisco Odair Vieira ; Lima, Sandra Machado de Souza ; Miyagaki, Olimpio Hiroshi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_1904_063823</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>de Paiva, Francisco Odair Vieira</creatorcontrib><creatorcontrib>Lima, Sandra Machado de Souza</creatorcontrib><creatorcontrib>Miyagaki, Olimpio Hiroshi</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>de Paiva, Francisco Odair Vieira</au><au>Lima, Sandra Machado de Souza</au><au>Miyagaki, Olimpio Hiroshi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence and multiplicity results for a class of non-linear Schr\"odinger equations with magnetic potential involving sign-changing non linearity</atitle><date>2019-04-12</date><risdate>2019</risdate><abstract>In this work we consider the following class of elliptic problems $$-
\Delta_A u + u = a(x) |u|^{q-2}u+b(x) |u|^{p-2}u , \mbox{ in } \mathbb{R}^N, $$
$u\in H^1_A (\mathbb{R}^N)$, with $2<q<p<2^*= \frac{2N}{N-2}$, $a(x)$ and
$b(x)$ are functions that can change signal and satisfy some additional
conditions; $u \in H^1_A(\mathbb{R}^N)$ and $A:\mathbb{R}^N \rightarrow
\mathbb{R}^N$ is a magnetic potential. Also using the Nehari method in
combination with other complementary arguments, we discuss the existence of
infinite solutions to the problem in question, varying the assumptions about
the weight functions.</abstract><doi>10.48550/arxiv.1904.06382</doi><oa>free_for_read</oa></addata></record> |
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| source | arXiv.org |
| subjects | Mathematics - Analysis of PDEs |
| title | Existence and multiplicity results for a class of non-linear Schr\"odinger equations with magnetic potential involving sign-changing non linearity |
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