Infinitely many solutions of Dirac equations with concave and convex nonlinearities
We consider non-periodic Dirac equations with nonlinearities which involve a combination of concave and convex terms. Using variational methods, we prove the existence of infinitely many large and small energy solutions. For small energy solutions, we establish a new critical point theorem which gen...
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| Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Physik 2021-02, Vol.72 (1), Article 39 |
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| container_title | Zeitschrift für angewandte Mathematik und Physik |
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| creator | Ding, Yanheng Dong, Xiaojing |
| description | We consider non-periodic Dirac equations with nonlinearities which involve a combination of concave and convex terms. Using variational methods, we prove the existence of infinitely many large and small energy solutions. For small energy solutions, we establish a new critical point theorem which generalize the dual Fountain Theorem of Bartsch and Willen, by using the index theory and the
P
-topology. Some non-periodic conditions on the whole space
R
3
are given in order to overcome the lack of compactness. |
| doi_str_mv | 10.1007/s00033-021-01472-3 |
| format | Article |
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P
-topology. Some non-periodic conditions on the whole space
R
3
are given in order to overcome the lack of compactness.</description><identifier>ISSN: 0044-2275</identifier><identifier>EISSN: 1420-9039</identifier><identifier>DOI: 10.1007/s00033-021-01472-3</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Critical point ; Engineering ; Mathematical analysis ; Mathematical Methods in Physics ; Theorems ; Theoretical and Applied Mechanics ; Topology ; Variational methods</subject><ispartof>Zeitschrift für angewandte Mathematik und Physik, 2021-02, Vol.72 (1), Article 39</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-f1adf191c01744d225c794221e2edfca420645faf19067149e3bf61aac7a7b613</citedby><cites>FETCH-LOGICAL-c319t-f1adf191c01744d225c794221e2edfca420645faf19067149e3bf61aac7a7b613</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/s00033-021-01472-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00033-021-01472-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Ding, Yanheng</creatorcontrib><creatorcontrib>Dong, Xiaojing</creatorcontrib><title>Infinitely many solutions of Dirac equations with concave and convex nonlinearities</title><title>Zeitschrift für angewandte Mathematik und Physik</title><addtitle>Z. Angew. Math. Phys</addtitle><description>We consider non-periodic Dirac equations with nonlinearities which involve a combination of concave and convex terms. Using variational methods, we prove the existence of infinitely many large and small energy solutions. For small energy solutions, we establish a new critical point theorem which generalize the dual Fountain Theorem of Bartsch and Willen, by using the index theory and the
P
-topology. Some non-periodic conditions on the whole space
R
3
are given in order to overcome the lack of compactness.</description><subject>Critical point</subject><subject>Engineering</subject><subject>Mathematical analysis</subject><subject>Mathematical Methods in Physics</subject><subject>Theorems</subject><subject>Theoretical and Applied Mechanics</subject><subject>Topology</subject><subject>Variational methods</subject><issn>0044-2275</issn><issn>1420-9039</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKt_wFPA8-pMkt10j1K_CgUP6jmk2URT2qRNdqv9925dwZunGYbnnRkeQi4RrhFA3mQA4LwAhgWgkKzgR2SEgkFRA6-PyQhAiIIxWZ6Ss5yXPS4R-Ii8zILzwbd2tadrHfY0x1XX-hgyjY7e-aQNtdtOD6NP335QE4PRO0t1aA79zn7REMPKB6uTb73N5-TE6VW2F791TN4e7l-nT8X8-XE2vZ0XhmPdFg5147BGAyiFaBgrjawFY2iZbZzR_feVKJ3uGagkitryhatQayO1XFTIx-Rq2LtJcdvZ3Kpl7FLoTyomJiXgRFayp9hAmRRzTtapTfJrnfYKQR3kqUGe6uWpH3mK9yE-hHIPh3eb_lb_k_oGKs5yaw</recordid><startdate>20210201</startdate><enddate>20210201</enddate><creator>Ding, Yanheng</creator><creator>Dong, Xiaojing</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210201</creationdate><title>Infinitely many solutions of Dirac equations with concave and convex nonlinearities</title><author>Ding, Yanheng ; Dong, Xiaojing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-f1adf191c01744d225c794221e2edfca420645faf19067149e3bf61aac7a7b613</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Critical point</topic><topic>Engineering</topic><topic>Mathematical analysis</topic><topic>Mathematical Methods in Physics</topic><topic>Theorems</topic><topic>Theoretical and Applied Mechanics</topic><topic>Topology</topic><topic>Variational methods</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ding, Yanheng</creatorcontrib><creatorcontrib>Dong, Xiaojing</creatorcontrib><collection>CrossRef</collection><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ding, Yanheng</au><au>Dong, Xiaojing</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Infinitely many solutions of Dirac equations with concave and convex nonlinearities</atitle><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle><stitle>Z. Angew. Math. Phys</stitle><date>2021-02-01</date><risdate>2021</risdate><volume>72</volume><issue>1</issue><artnum>39</artnum><issn>0044-2275</issn><eissn>1420-9039</eissn><abstract>We consider non-periodic Dirac equations with nonlinearities which involve a combination of concave and convex terms. Using variational methods, we prove the existence of infinitely many large and small energy solutions. For small energy solutions, we establish a new critical point theorem which generalize the dual Fountain Theorem of Bartsch and Willen, by using the index theory and the
P
-topology. Some non-periodic conditions on the whole space
R
3
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| subjects | Critical point Engineering Mathematical analysis Mathematical Methods in Physics Theorems Theoretical and Applied Mechanics Topology Variational methods |
| title | Infinitely many solutions of Dirac equations with concave and convex nonlinearities |
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