On a Nonclassical Eigenvalue Problem with Nonlinearizable Solutions
We study a nonlinear eigenvalue problem of a special form arising in electrodynamics. The problem is posed for a system of two equations with boundary conditions of the first kind and two additional local conditions. There is one spectral parameter in the problem, and two more parameters, which are...
Saved in:
| Published in | Differential equations Vol. 59; no. 3; pp. 301 - 311 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.03.2023
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | We study a nonlinear eigenvalue problem of a special form arising in electrodynamics. The problem is posed for a system of two equations with boundary conditions of the first kind and two additional local conditions. There is one spectral parameter in the problem, and two more parameters, which are subject to an additional constraint, occur in the above-mentioned local conditions. Thus, there are two unknown parameters in the problem: one is the spectral parameter, and the other is some additional parameter, chosen so as to ensure that there exists a nontrivial solution of the problem in question. The existence of nonlinearizable solutions of the problem is proved. |
|---|---|
| AbstractList | We study a nonlinear eigenvalue problem of a special form arising in electrodynamics. The problem is posed for a system of two equations with boundary conditions of the first kind and two additional local conditions. There is one spectral parameter in the problem, and two more parameters, which are subject to an additional constraint, occur in the above-mentioned local conditions. Thus, there are two unknown parameters in the problem: one is the spectral parameter, and the other is some additional parameter, chosen so as to ensure that there exists a nontrivial solution of the problem in question. The existence of nonlinearizable solutions of the problem is proved. We study a nonlinear eigenvalue problem of a special form arising in electrodynamics. Theproblem is posed for a system of two equations with boundary conditions of the first kind and twoadditional local conditions. There is one spectral parameter in the problem, and two moreparameters, which are subject to an additional constraint, occur in the above-mentioned localconditions. Thus, there are two unknown parameters in the problem: one is the spectralparameter, and the other is some additional parameter, chosen so as to ensure that there exists anontrivial solution of the problem in question. The existence of nonlinearizable solutions of theproblem is proved. |
| Audience | Academic |
| Author | Martynova, V. Yu Valovik, D. V. |
| Author_xml | – sequence: 1 givenname: D. V. surname: Valovik fullname: Valovik, D. V. email: dvalovik@mail.ru organization: Penza State University – sequence: 2 givenname: V. Yu surname: Martynova fullname: Martynova, V. Yu email: lynxbax@mail.ru organization: Penza State University |
| BookMark | eNp9kFtLAzEQhYMo2FZ_gG8LPm_NpcluHkupFyhWaN-X2Wy2pqRJTbaK_nqzVBAUZR4G5pxvhjlDdOq80whdETwmhE1uVhgTSoUglGGGMWUnaEAELnOGS3aKBr2c9_o5Gsa4xRjLgvABmi1dBtmjd8pCjEaBzeZmo90r2IPOnoKvrd5lb6Z77k3WOA3BfECaZitvD53xLl6gsxZs1JdffYTWt_P17D5fLO8eZtNFrhjnXa6kFDUQyotaQM0YgVK1LWOFBgEci4Y1dIJxLQrQupwI0jBFa17ICZQta9gIXR_X7oN_OejYVVt_CC5drGhJieRSYplc46NrA1ZXxrW-C6BSNXpnVAqtNWk-LTjhkpeUJqA4Air4GINuK2U66B9LoLEVwVWfcPUr4USSH-Q-mB2E938ZemRi8rqNDt9P_A19AqCmjJQ |
| CitedBy_id | crossref_primary_10_31857_S0374064124040035 crossref_primary_10_1134_S0012266124040049 |
| Cites_doi | 10.1134/S0012266120020032 10.1007/978-3-319-12748-4 10.21685/2072-3040-2021-4-3 10.1090/cln/010 10.1016/B978-0-444-88359-9.50008-9 |
| ContentType | Journal Article |
| Copyright | Pleiades Publishing, Ltd. 2023 COPYRIGHT 2023 Springer Pleiades Publishing, Ltd. 2023. |
| Copyright_xml | – notice: Pleiades Publishing, Ltd. 2023 – notice: COPYRIGHT 2023 Springer – notice: Pleiades Publishing, Ltd. 2023. |
| DBID | AAYXX CITATION 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| DOI | 10.1134/S0012266123030023 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Civil Engineering Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Sciences (General) Mathematics |
| EISSN | 1608-3083 |
| EndPage | 311 |
| ExternalDocumentID | A751595822 10_1134_S0012266123030023 |
| GroupedDBID | --Z -5D -5G -BR -EM -Y2 -~C -~X .86 .VR 04Q 04W 06D 0R~ 0VY 1N0 29G 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 3V. 4.4 408 409 40D 40E 5GY 5VS 67Z 6NX 6TJ 78A 7WY 8FE 8FG 8FL 8G5 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDBF ABDZT ABECU ABEFU ABFTV ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABLLD ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACNCT ACOKC ACOMO ACPIV ACUHS ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AETLH AEVLU AEXYK AFBBN AFFNX AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARMRJ ASPBG AVWKF AXYYD AZFZN AZQEC B-. B0M BA0 BAPOH BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 DWQXO EAD EAP EBLON EBS EIOEI EJD EMK EPL ESBYG ESX FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GUQSH GXS H13 HCIFZ HF~ HG6 HMJXF HQYDN HRMNR HVGLF HZ~ IAO IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C JBSCW JCJTX JZLTJ K60 K6V K6~ K7- KDC KOV L6V LAK LLZTM M0C M0N M2O M4Y M7S MA- N2Q NB0 NPVJJ NQJWS NU0 O9- O93 O9J OAM OHT OVD P2P P62 P9R PADUT PF0 PKN PQBIZ PQBZA PQQKQ PROAC PT4 PTHSS Q2X QOS R89 R9I RNI RNS ROL RPX RSV RZC RZE S16 S1Z S27 S3B SAP SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TEORI TN5 TSG TSK TSV TUC TUS TWZ U2A UG4 UOJIU UPT UTJUX UZXMN VC2 VFIZW VH1 W23 W48 WH7 WK8 XU3 YLTOR ~8M ~A9 AAPKM AAYXX ABDBE ABFSG ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR CITATION PHGZM PHGZT AEIIB 7SC 7TB 8FD ABRTQ FR3 JQ2 KR7 L7M L~C L~D |
| ID | FETCH-LOGICAL-c355t-c996ba1257b6ab331a8cff337ea6a506d3d2400b67aee8461d3c2b5794a8f3d3 |
| IEDL.DBID | U2A |
| ISSN | 0012-2661 |
| IngestDate | Fri Jul 25 19:25:59 EDT 2025 Tue Jun 10 21:12:17 EDT 2025 Tue Jul 01 00:39:03 EDT 2025 Thu Apr 24 22:51:53 EDT 2025 Fri Feb 21 02:43:22 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c355t-c996ba1257b6ab331a8cff337ea6a506d3d2400b67aee8461d3c2b5794a8f3d3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2821959909 |
| PQPubID | 54032 |
| PageCount | 11 |
| ParticipantIDs | proquest_journals_2821959909 gale_infotracacademiconefile_A751595822 crossref_citationtrail_10_1134_S0012266123030023 crossref_primary_10_1134_S0012266123030023 springer_journals_10_1134_S0012266123030023 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2023-03-01 |
| PublicationDateYYYYMMDD | 2023-03-01 |
| PublicationDate_xml | – month: 03 year: 2023 text: 2023-03-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Moscow |
| PublicationPlace_xml | – name: Moscow – name: New York |
| PublicationTitle | Differential equations |
| PublicationTitleAbbrev | Diff Equat |
| PublicationYear | 2023 |
| Publisher | Pleiades Publishing Springer Springer Nature B.V |
| Publisher_xml | – name: Pleiades Publishing – name: Springer – name: Springer Nature B.V |
| References | CR11 Petrovskii (CR2) 1984 CR10 Pontryagin (CR3) 1961 Hartman (CR4) 1964 Marchenko (CR6) 1977 Kurseeva, Moskaleva, Valovik (CR1) 2020; 119 CR7 Landau, Livshits (CR8) 1982 Boyd (CR9) 2003 Valovik (CR5) 2020; 56 CR12 2490_CR7 R.W. Boyd (2490_CR9) 2003 2490_CR11 I.G. Petrovskii (2490_CR2) 1984 V.A. Marchenko (2490_CR6) 1977 2490_CR10 L.D. Landau (2490_CR8) 1982 2490_CR12 L.S. Pontryagin (2490_CR3) 1961 D.V. Valovik (2490_CR5) 2020; 56 V.Yu. Kurseeva (2490_CR1) 2020; 119 P. Hartman (2490_CR4) 1964 |
| References_xml | – volume: 119 start-page: 39 issue: 1–2 year: 2020 end-page: 59 ident: CR1 article-title: Asymptotical analysis of a nonlinear Sturm–Liouville problem: Linearisable and non-linearisable solutions publication-title: Asymptot. Anal. – year: 2003 ident: CR9 publication-title: Nonlinear Optics – year: 1964 ident: CR4 publication-title: Ordinary Differential Equations – ident: CR7 – volume: 56 start-page: 175 issue: 2 year: 2020 end-page: 189 ident: CR5 article-title: Study of a nonlinear eigenvalue problem by the integral characteristic equation method publication-title: Differ. Equations doi: 10.1134/S0012266120020032 – year: 1977 ident: CR6 publication-title: Operatory Shturma–Liuvillya i ikh prilozheniya (Sturm–Liouville Operators and Applications) – year: 1984 ident: CR2 publication-title: Lektsii po teorii obyknovennykh differentsial’nykh uravnenii (Lectures on the Theory of Ordinary Differential Equations) – year: 1982 ident: CR8 publication-title: Elekrodinamika sploshnykh sred (Electrodynamics of Continuous Media) – ident: CR12 – year: 1961 ident: CR3 publication-title: Obyknovennye differentsial’nye uravneniya (Ordinary Differential Equations) – ident: CR10 – ident: CR11 – ident: 2490_CR10 doi: 10.1007/978-3-319-12748-4 – volume-title: Ordinary Differential Equations year: 1964 ident: 2490_CR4 – volume-title: Operatory Shturma–Liuvillya i ikh prilozheniya (Sturm–Liouville Operators and Applications) year: 1977 ident: 2490_CR6 – volume-title: Lektsii po teorii obyknovennykh differentsial’nykh uravnenii (Lectures on the Theory of Ordinary Differential Equations) year: 1984 ident: 2490_CR2 – volume: 56 start-page: 175 issue: 2 year: 2020 ident: 2490_CR5 publication-title: Differ. Equations doi: 10.1134/S0012266120020032 – ident: 2490_CR12 doi: 10.21685/2072-3040-2021-4-3 – volume: 119 start-page: 39 issue: 1–2 year: 2020 ident: 2490_CR1 publication-title: Asymptot. Anal. – volume-title: Elekrodinamika sploshnykh sred (Electrodynamics of Continuous Media) year: 1982 ident: 2490_CR8 – volume-title: Nonlinear Optics year: 2003 ident: 2490_CR9 – ident: 2490_CR11 doi: 10.1090/cln/010 – ident: 2490_CR7 doi: 10.1016/B978-0-444-88359-9.50008-9 – volume-title: Obyknovennye differentsial’nye uravneniya (Ordinary Differential Equations) year: 1961 ident: 2490_CR3 |
| SSID | ssj0009715 |
| Score | 2.2666135 |
| Snippet | We study a nonlinear eigenvalue problem of a special form arising in electrodynamics. The problem is posed for a system of two equations with boundary... We study a nonlinear eigenvalue problem of a special form arising in electrodynamics. Theproblem is posed for a system of two equations with boundary... |
| SourceID | proquest gale crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 301 |
| SubjectTerms | Boundary conditions Difference and Functional Equations Differential equations Eigenvalues Electrodynamics Mathematics Mathematics and Statistics Ordinary Differential Equations Parameters Partial Differential Equations |
| Title | On a Nonclassical Eigenvalue Problem with Nonlinearizable Solutions |
| URI | https://link.springer.com/article/10.1134/S0012266123030023 https://www.proquest.com/docview/2821959909 |
| Volume | 59 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8MwDLZ4XOCAYIAojykHJF6q1DZNH8cNNibQgANI41S5WXpCHWLjwq_HXtNNMEDi1EOdtIrj-HMSfwY4VmkRy7xQrpKKAhRNlo7IicAJBsbDSKHhfcj-XdR7Cm8GamDzuMf1bff6SHK6Uld1R0LO6fUDdicEmiW7mmVYVRy60yR-Clpzpt24LlsQuCxujzJ_7OKLM_q-JC-cjU5dTncTNixWFK1KuVuwZMoGrPdnRKvjBmxZ2xyLU0sgfbYNl_elQHE3KjVDY9aC6DDpJhN7G_FQlZARvAPLQowzKWD-4BwqMdsl24HHbufxsufaYgmuJsgwcTUFLjkSXInzCHMpfUx0UUgZG4xQedFQDvm6aB7FaAyBDn8odZArMkdMCjmUu7BSjkqzB0IlaSGLAEmFGBa-xCRUBFN06kWpQt844NWDlmlLJM71LF6yaUAhw2xhnB04nzV5rVg0_hI-YU1kbGHUr0abKEB_x1xVWStmDKYI2ThwWCsrs6Y3ziiGZMKc1EsduKgVOH_962f3_yV9AGtceL66jXYIK5O3d3NE8GSSN2G11b5qd_l5_XzbaU6n5ye0H9j2 |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8MwDLZgHIADYgPEYEAOSLxUqW2aPo4TYhqwDQ6btFvlZukJdYiNC78ee02HeEqc66ZVHMefE_szwKlK8khmuXKUVBSgaLJ0RC4EjtE3LoYKDZ9D9gdhdxTcjdXY1nHPqmz36kpysVOXfUcCrun1fHYnBJolu5pVWCMsEHMe18hvfzDtRlXbAt9hcXuV-eMQn5zR1y35293owuV0tmHLYkXRLpVbhxVTNGCzvyRanTWgbm1zJs4tgfTFDlw_FALFYFpohsasBXHDpJtM7G3EY9lCRvAJLAsxzqSA-Y1rqMTylGwXhp2b4XXXsc0SHE2QYe5oClwyJLgSZSFmUnoY6zyXMjIYonLDiZxwumgWRmgMgQ5vIrWfKTJHjHM5kXtQK6aF2Qeh4iSXuY-kQgxyT2IcKIIpOnHDRKFnmuBWk5ZqSyTO_Sye0kVAIYP02zw34XL5ynPJovGX8BlrImULo3E12kIB-jvmqkrbEWMwRcimCa1KWak1vVlKMSQT5iRu0oSrSoEfj3_97MG_pE9gvTvs99Le7eD-EDa4CX2ZmdaC2vzl1RwRVJlnx4ul-Q58gNjj |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8MwDLZ4SAgOiKcYDMgBiZcq2qbp4zjBJp6DA0jcKjdNTqhDbFz49dhrOsRT4lw3reI4_hzHnwH2VGYTWVjlKakoQNFk6YhcCJxiaHyMFRo-h7zpx-cP0eWjenR9TofNbfcmJVnXNDBLUzU6eS6t60EScX1vELJrIQAt2e1MwyztxgEv64ew88G6mzQtDEKPxV1a88chPjmmr9vztzzp2P30lmDR4UbRqRW9DFOmWoGFmwnp6nAFlp2dDsWBI5M-XIXT20qg6A8qzTCZNSK6TMDJJN9G3NXtZASfxrIQY04Knt-4nkpMTszW4L7XvT8991zjBE8TfBh5moKYAgm6JEWMhZQBptpaKRODMSo_LmXJV0eLOEFjCIAEpdRhocg0MbWylOswUw0qswFCpZmVNkRSJ0Y2kJhGiiCLzvw4UxiYFvjNpOXakYpzb4unfBxcyCj_Ns8tOJq88lwzavwlvM-ayNnaaFyNrmiA_o55q_JOwnhMEcppQbtRVu7McJhTPMnkOZmfteC4UeDH418_u_kv6V2Yuzvr5dcX_astmOd-9PUltTbMjF5ezTahllGxM16Z73Dz3R8 |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+a+Nonclassical+Eigenvalue+Problem+with+Nonlinearizable+Solutions&rft.jtitle=Differential+equations&rft.au=Valovik%2C+D+V&rft.au=Yu%2C+Martynova+V&rft.date=2023-03-01&rft.pub=Springer+Nature+B.V&rft.issn=0012-2661&rft.eissn=1608-3083&rft.volume=59&rft.issue=3&rft.spage=301&rft.epage=311&rft_id=info:doi/10.1134%2FS0012266123030023&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0012-2661&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0012-2661&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0012-2661&client=summon |