Augšējo un apakšējo funkciju metodes pielietojums otrās kārtas robežproblēmu atrisināmības pētīšanā
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Latvijas Universitāte
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lav
Abstract
Darbā tiek izpētīta otrās kārtas periodiskā robežproblēma parastajam diferenciālvienādojumam un tās atrisināmība, izmantojot augšējo un apakšējo funkciju metodi. Tiek apskatīta periodiskā robežproblēma lineāram homogēnam vienādojumam un atbilstošam nehomogēnam vienādojumam un šie rezultāti tiek izmantoti kā palīgrezultāti turpmākajā pētījumā. Tiek aplūkota Konti teorēma, uz kuras pamata balstās bakalaura darba galveno rezultātu pierādījumi. Tiek demonstrēti piemēri, kuri ilustrē bakalaura darba galvenos rezultātus.
The bachelor's thesis investigates the second order periodic boundary value problem for the ordinary differential equation and its solvability using the method of upper and lower functions. The periodic boundary value problem for a linear homogeneous equation and the corresponding nonhomogeneous equation is considered and these results are used as auxiliary results in the further study. The Conti theorem, which is a base of the proofs' of our main results, is also considered. Examples are shown to illustrate the main results of the bachelor's thesis.
The bachelor's thesis investigates the second order periodic boundary value problem for the ordinary differential equation and its solvability using the method of upper and lower functions. The periodic boundary value problem for a linear homogeneous equation and the corresponding nonhomogeneous equation is considered and these results are used as auxiliary results in the further study. The Conti theorem, which is a base of the proofs' of our main results, is also considered. Examples are shown to illustrate the main results of the bachelor's thesis.