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https://open.uns.ac.rs/handle/123456789/27386| Title: | Kvalitativna analiza nekih klasa nelinearnih diferencnih jednačina The Qualitative Analysis of Some Classes of Nonlinear DifferenceEquations |
Authors: | Iričanin Bratislav | Keywords: | Diferencne jednačine, kvalitativna analiza, nelinarne diferencne jednačine, sistemi diferencnih jednačina; ograničeni karakter, lokalna stabilnost, globalna atraktivnost, periodičnost, asimptotska periodičnost, asimptotsko ponašanje.;Di®erence equations, qualitative analysis, nonlinear di®erence equations, systems of di®erence equations; boundedness character, local stability, global attractiveness, periodicity, asymptotic periodicity,asymptotic behavior. | Issue Date: | 20-Jun-2009 | Publisher: | Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu University of Novi Sad, Faculty of Sciences at Novi Sad |
Abstract: | <p>U doktorskoj disertaciji autor se bavi veoma aktuelnom problematikom tretiranja nelinearnih diferencnih jednačina. U pitanju su različite klase racionalnih jednačina višeg reda, zatim tzv.max jednačina, kao i neki sistemi nelinearnih diferencnih jednačina. Metodima matematičke analize vrši se kvalitativna analiza, što podrazumeva ispitivanje asimptotskog ponašanja rešenja jednačina. Posebno veliko interesovanje pobuđuju ograničenost, konvergencija, stabilnost, oscilatornost, asimptotska periodičnost i globalna atraktivnost rešenja. Posle kraćeg uvoda,autor u narednih 12 glava ispituje osobine različitih klasa jednačina,uključujući i kritičko razmatranje rezultata drugih autora, dok u završnoj glavi - zaključku - finalizuje ovo istraživanje. U disertaciji je (viii+129 standardnih strana) ponunjen veći broj novih originalnih naučnih rezultata, od kojih su neki već i publikovani od strane autora. Iscrpan spisak adekvatne savremene literature (od 140 referenci, ukqučijući i pet radova Autora) ukazuje na temeljitost u tretiranju problema i garantuje originalnost dobijenih rezultata.</p> <p><span style="left: 167.727px; top: 464.578px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(1.08189);">In this</span><span style="left: 216.18px; top: 464.578px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(0.991819);">Dissertation</span><span style="left: 297.763px; top: 464.578px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(1.00958);">Author deals with the very actual problem of nonlinear</span><span style="left: 167.727px; top: 482.65px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(0.994548);">difference equations treatment. The focus is on different classes of higher-</span><span style="left: 167.727px; top: 500.709px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(1.01362);">-order rational type equations, then so-called</span><span style="left: 468.891px; top: 500.709px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(0.931663);">max</span><span style="left: 500.673px; top: 500.709px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(0.981811);">– equations, as well as</span><span style="left: 167.727px; top: 518.78px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(0.988389);">some systems of nonlinear difference equations. The qualitative analysis is</span><span style="left: 167.727px; top: 536.839px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(0.954845);">performed by means of mathematical analysis methods, which implies the in-</span><span style="left: 167.727px; top: 554.91px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(0.998746);">vestigation of the asymptotic behaviour of equations’ solutions. Particularly</span><span style="left: 167.727px; top: 572.969px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(1.02439);">great interest motivates boundedness, convergence, stability, periodicity,</span><span style="left: 167.727px; top: 591.041px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(0.994563);">asymptotic periodicity and global attractiveness of the solution. After a brief</span><span style="left: 167.727px; top: 609.099px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(0.988398);">introduction, in the next 12 chapters Author investigates different classes of</span><span style="left: 167.727px; top: 627.171px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(1.04223);">equations, including the critical treatment of other author’s results; con-</span><span style="left: 167.727px; top: 645.229px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(1.01744);">cluding chapter finalizes this research. On</span><span style="left: 458.902px; top: 645.229px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(1.25509);">viii</span><span style="left: 481.401px; top: 645.229px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(1.01603);">+129 standard pages the</span><span style="left: 167.727px; top: 663.301px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(0.991819);">Dissertation</span><span style="left: 249.883px; top: 663.301px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(0.978266);">has offered a considerable amount of new original scientific re-</span><span style="left: 167.727px; top: 681.372px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(1.05138);">sults, some of which are already published by the Author. The detailed</span><span style="left: 167.727px; top: 699.431px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(1.03545);">list of adequate up-to-date literature (140 references, including 5 Author’</span><span style="left: 167.727px; top: 717.503px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(0.994554);">papers) points out the solidity of the research, and thus guarantees the ori-</span><span style="left: 167.727px; top: 735.561px; font-size: 14.5507px; font-family: sans-serif; transform: scaleX(1.01993);">ginality of obtained results.</span></p> |
URI: | https://open.uns.ac.rs/handle/123456789/27386 |
| Appears in Collections: | PMF Teze/Theses |
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