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Sturm-Liouvilleov problem
Acta mathematica Spalatensia. Series didactica, 4 (2021); 97-111. https://doi.org/10.32817/amssd.4.4.7
Čatipović, Marija; Krešić-Jurić, Saša

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Čatipović, M. & Krešić Jurić, S.. Sturm-Liouvilleov problem. Acta mathematica Spalatensia. Series didactica, 4., 97-111. doi: 10.32817/amssd.4.4.7

Čatipović, Marija and Saša Krešić Jurić. "Sturm-Liouvilleov problem." Acta mathematica Spalatensia. Series didactica, vol. 4, pp. 97-111. https://doi.org/10.32817/amssd.4.4.7

Čatipović, Marija and Saša Krešić Jurić. "Sturm-Liouvilleov problem." Acta mathematica Spalatensia. Series didactica 4 97-111. https://doi.org/10.32817/amssd.4.4.7

Čatipović, M. and Krešić Jurić, S. 'Sturm-Liouvilleov problem', Acta mathematica Spalatensia. Series didactica, 4, pp. 97-111. doi: 10.32817/amssd.4.4.7

Čatipović M, Krešić Jurić S. Sturm-Liouvilleov problem. Acta mathematica Spalatensia. Series didactica [Internet]. [cited 2025 April 02];4:97-111. doi: 10.32817/amssd.4.4.7

M. Čatipović and S. Krešić Jurić, "Sturm-Liouvilleov problem", Acta mathematica Spalatensia. Series didactica, vol. 4, pp. 97-111. [Online]. Available at: https://urn.nsk.hr/urn:nbn:hr:179:107225. [Accessed: 02 April 2025]

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Metadata
Title (croatian)Sturm-Liouvilleov problem
AuthorMarija Čatipović
AuthorSaša Krešić-Jurić
Author's institutionUniversity of Split
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture
Author's institutionUniversity of Split
Faculty of Science
(Department of Mathematics)
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract (croatian)
Klasična Sturm-Liouvilleova jednadžba, nazvana po Jacquesu Sturmu i Josephu Liouvilleu, je obična diferencijalna jednadžba drugog reda posebnog oblika u ovisnosti o parametru lambda. Pronalaženje te vrijednosti za koju postoje netrivijalna rješenja jednadžbe i koja zadovoljavaju rubne uvjete je dio problema kojeg nazivamo Sturm-Liouvilleov problem. Pokazat ćemo da se proizvoljni linearni operator drugog reda može transformirati u Sturm-Liouvilleov operator tj. da je Sturm-Liouvilleov operator kanonski oblik diferencijalnog operatora drugog reda. Vlastite vrijednosti regularnog Sturm-Liouvilleovog problema su realne, prebrojive i tvore strogo rastući neomeđeni niz. Također, za svaku vlastitu vrijednost postoji odgovarajuća vlastita funkcija jedinstveno određena do na multiplikativnu konstantu koja ima točno n nultočki u intervalu [a; b]. Ovo je jedan od fundamentalnih rezultata za Sturm-Liouvilleove operatore.
Keywords (croatian)
Languagecroatian
Publication typeProfessional paper - Professional paper
Publication statusPublished
Peer reviewPeer review - domestic
Publication versionPublished version
Journal titleActa mathematica Spalatensia. Series didactica
Numberingvol. 4, pp. 97-111
p-ISSN2623-6125
e-ISSN2623-5803
DOIhttps://doi.org/10.32817/amssd.4.4.7
URN:NBNurn:nbn:hr:179:107225
Accepted2021-01-14
Type of resourceText
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-05-01 12:49:27