Asimptotska svojstva rešenja jednačina Emden-Faulera i njihovih uopštenja

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Asimptotska svojstva rešenja jednačina Emden-Faulera i njihovih uopštenja

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dc.contributor.advisor Krtinić, Đorđe
dc.contributor.author Mikić, Marija
dc.date.accessioned 2018-03-05T14:34:23Z
dc.date.available 2018-03-05T14:34:23Z
dc.date.issued 2017
dc.identifier.uri http://hdl.handle.net/123456789/4655
dc.description.abstract The subject of this dissertation is the investigation of asymptotic properties of solutions for di erential equations of Emden-Fowler type and their generalizations. The eld to which this dissertation belongs is a Qualitative theory of ordinary di e- rential equations. Emden-Fowler di erential equation has the form (t u0(t))0 t u (t) = 0 ; where ; ; 2 R. With some changes of the variables, this di erential equation can be reduced to the equations y00 􀀀 xay = 0 and y00 + xay = 0. Firstly, in this dissertation, the di erential equation y00 = xay ; where a; 2 R was observed. The conditions, which provide that this equation has in nitely many solutions de ned in some neighborhood of zero, were described here, both with the conditions, which guarantee the existence of in nitely many solutions with certain asymptotic behavior. Also, a complete picture of asymptotic behavior of solutions of equation along the positive parts of both axes is given. The conditions, which assure existence and unique solvability of solution of the Cauchy problem for this equation, were shown in the cases when the familiar theory can't be applied. In some cases, asymptotic formulas for solutions were obtained. The di erential equation y00 = 􀀀xay ; where a 2 R i < 0 ; has also been taken into consideration. The conditions, which assure the existence of in nitely many solutions of observed equation tending to zero as x ! 0+, were obtained. The conditions, which assure the unique solvability of the Cauchy problem for generalized Emden-Fowler equation y00 = q(x)f(y(x)); lim x!0+ y(x) = 0; lim x!0+ y0(x) = ; were described, for any > 0 and functions f and q which satisfy certain conditions. The given results generalize the results both for sublinear Emden-Fowler di erential equation (i.e. case when 0 < < 1) and the case when < 0. In literature, it is very rare to nd the conditions for di erent values of the para- metar which appears in the equations of Emden-Fowler type. In this dissertation, the results for sublinear and superlinear di erential equation Emden-Fowler, as well as the case when < 0, are presented. Therefore, the story of the asymptotic be- havior of solutions of the observed equation is "almost complited". en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2018-03-05T14:34:23Z No. of bitstreams: 1 Marija_Mikic_disertacija_MTF.pdf: 1461229 bytes, checksum: 18552265648ff22bdeee50359fd0d767 (MD5) en
dc.description.provenance Made available in DSpace on 2018-03-05T14:34:23Z (GMT). No. of bitstreams: 1 Marija_Mikic_disertacija_MTF.pdf: 1461229 bytes, checksum: 18552265648ff22bdeee50359fd0d767 (MD5) Previous issue date: 2017 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title Asimptotska svojstva rešenja jednačina Emden-Faulera i njihovih uopštenja en_US
mf.author.birth-date 1987-05-12
mf.author.birth-place Smederevska Palanka en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srpkinja en_US
mf.subject.area Mathematics en_US
mf.subject.keywords Emden-Fowler di erential equation, superlinear equation, sublinear equation, asymptotic behavior of solutions, Cauchy problem. en_US
mf.subject.subarea Differential equations en_US
mf.subject.msc 34A34, 34E10.
mf.contributor.committee Krtinić, Đorđe
mf.contributor.committee Lažetić, Nebojša
mf.contributor.committee Spalević, Miodrag
mf.university.faculty Mathematical Faculty en_US
mf.document.references 17 en_US
mf.document.pages 55 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.subject.udc 517.911, 517.925.4(043.3).
mf.university Belgrade University en_US

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