2018-ci ild\u0259 \u201cRiyazi fizika t\u0259nlikl\u0259ri\u201d \u015f\u00f6b\u0259sind\u0259 plana \u0259sas\u0259n t\u0259sdiq olunmu\u015f “Riyazi fizika m\u0259s\u0259l\u0259l\u0259rinin birqiym\u0259tli h\u0259ll olunmas\u0131 v\u0259 h\u0259ll\u0259rinin keyfiyy\u0259t xass\u0259l\u0259ri\u201d\u00a0 m\u00f6vzusu \u00fczr\u0259 on bir istiqam\u0259td\u0259 elmi t\u0259dqiqat i\u015fi apar\u0131l\u0131r.<\/p>\n
1) \u0130\u015e: \u201dKvazielliptik operatorun m\u0259nfi spektrinin ara\u015fd\u0131r\u0131lmas\u0131\u201d.<\/p>\n
\u0130cra\u00e7\u0131: AMEA-n\u0131n m\u00fcxbir \u00fczv\u00fc, prof. R.V. H\u00fcseynov.<\/p>\n
Hesabat d\u00f6vr\u00fcnd\u0259 y\u00fcks\u0259k t\u0259rtibli elliptik t\u0259nlikl\u0259r v\u0259 b\u0259zi kvazielliptik t\u0259nlikl\u0259r \u00fc\u00e7\u00fcn spektr \u00f6yr\u0259nilir. X\u00fcsusil\u0259 stasionar \u015eredinger operatorunun y\u00fcks\u0259k t\u0259rtibli analoqlar\u0131 t\u0259dqiq edilir. Bu zaman diferensial operator v\u0259 verilmi\u015f Q(x) potensial\u0131n\u0131n m\u00fcxt\u0259lif hallar\u0131na g\u00f6r\u0259 m\u0259nfi spektr \u00f6yr\u0259nilir. Potensial \u00fcz\u0259rin\u0259 m\u0259nfi spektrin sonlu v\u0259 sonsuz olmas\u0131n\u0131 t\u0259min ed\u0259 bil\u0259c\u0259k hans\u0131 \u015f\u0259rtl\u0259rin qoyulmas\u0131 ara\u015fd\u0131r\u0131l\u0131r.<\/p>\n
2) \u0130\u015e: \u201dYarimx\u0259tti elliptik t\u0259nlik \u00fc\u00e7\u00fcn bir t\u0259rs m\u0259s\u0259l\u0259nin t\u0259qribi h\u0259ll olunmas\u0131\u201d.
\n\u0130cra\u00e7\u0131: prof. \u018f.Y. Axundov.
\nYar\u0131mx\u0259tti elliptik t\u0259nlikl\u0259r sisteminin sa\u011f t\u0259r\u0259find\u0259ki nam\u0259lum \u0259msallar\u0131n tap\u0131lmas\u0131 haqq\u0131nda t\u0259rs m\u0259s\u0259l\u0259y\u0259 bax\u0131lm\u0131\u015f v\u0259 ard\u0131c\u0131l yax\u0131nla\u015fma \u00fcsulu il\u0259 bax\u0131lan m\u0259s\u0259l\u0259 h\u0259ll edilmi\u015f, t\u0259qribi h\u0259llin h\u0259nd\u0259si silsil\u0259 s\u00fcr\u0259ti il\u0259 d\u0259qiq h\u0259ll\u0259 y\u0131\u011f\u0131lmas\u0131 g\u00f6st\u0259rilmi\u015f, h\u0259llin varl\u0131\u011f\u0131, yegan\u0259liyi v\u0259 dayanaql\u0131\u011f\u0131 isbat olunmu\u015fdur.<\/p>\n
3) \u0130\u015e: \u201dHardi-Sobolev-Puankare tipli inteqral b\u0259rab\u0259rsizlikl\u0259r v\u0259 onun t\u0259tbiql\u0259ri. Qeyri-m\u00fcnt\u0259z\u0259m c\u0131rla\u015fan elliptik v\u0259 parabolik tipli x\u00fcsusi t\u00f6r\u0259m\u0259li t\u0259nlikl\u0259rin keyfiyy\u0259t xass\u0259l\u0259ri\u201d.
\n\u0130cra\u00e7\u0131: prof. F.\u0130. M\u0259mm\u0259dov.<\/p>\n
Hesabat d\u00f6vr\u00fcnd\u0259 bir sinif qeyri-m\u00fcnt\u0259z\u0259m c\u0131rla\u015fmal\u0131 elliptik t\u0259nlikl\u0259r\u0259 bax\u0131lm\u0131\u015fd\u0131r. H\u0259min t\u0259nlikl\u0259rin h\u0259ll\u0259ri \u00fc\u00e7\u00fcn keyfiyy\u0259t xass\u0259l\u0259ri t\u0259dqiq edilmi\u015fdir. Bel\u0259 ki, h\u0259ll\u0259rin H\u00f6lder normas\u0131n\u0131n aprior qiym\u0259tl\u0259ndirilm\u0259si isbat edilmi\u015fdir.<\/p>\n
4) \u0130\u015e: \u201dQeyri-divergent strukturlu 2-ci t\u0259rtib parabolik t\u0259nlikl\u0259rin h\u0259ll\u0259rinin b\u0259zi keyfiyy\u0259t xass\u0259l\u0259ri\u201d.
\n\u0130cra\u00e7\u0131: \u018f.F. Quliyev.
\nParabolik t\u0259nlikl\u0259rin sup, super h\u0259ll\u0259ri olan Veyer\u015ftrass tip n\u00fcv\u0259l\u0259r \u00fc\u00e7\u00fcn paraboloidl\u0259rd\u0259 n\u00fcv\u0259nin polyusdak\u0131 qiym\u0259ti il\u0259 qiym\u0259tl\u0259ndiril\u0259n iki t\u0259r\u0259fli ekvivalent qiym\u0259tl\u0259ndirm\u0259l\u0259r al\u0131nm\u0131\u015f v\u0259 al\u0131nm\u0131\u015f n\u0259tic\u0259l\u0259r t\u0259tbiq olunaraq, ikinci t\u0259rtib parabolik t\u0259nlkl\u0259rin h\u0259ll\u0259ri \u00fc\u00e7\u00fcn art\u0131m tip teorem al\u0131nm\u0131\u015fd\u0131r.<\/p>\n
5) \u0130\u015e: \u201dSinqulyar potensiall\u0131 elliptik v\u0259 parabolik t\u0259nlikl\u0259r v\u0259 yar\u0131mx\u0259tti t\u0259nlikl\u0259r sisteminin xarici oblastda qlobal h\u0259llinin yoxlu\u011fu\u201d.<\/p>\n
\u0130cra\u00e7\u0131: dos. \u015e.H. Ba\u011f\u0131rov.<\/p>\n
Xarici oblastda yar\u0131mx\u0259tti elliptik v\u0259 parabolik t\u0259nlikl\u0259rin m\u00fcsb\u0259t qlobal h\u0259ll\u0259rinin varl\u0131\u011f\u0131 m\u0259s\u0259l\u0259si t\u0259dqiq edilmi\u015fdir. \u015ear\u0131n xarici olan oblastda ba\u015f hiss\u0259si biharmonik operator olan sinqulyar potensiall\u0131 yar\u0131mx\u0259tti elliptik t\u0259nliyin m\u00fcsb\u0259t qlobal h\u0259llinin yoxlu\u011fu m\u0259s\u0259l\u0259si \u00f6yr\u0259nilmi\u015f v\u0259 h\u0259llin yoxlu\u011funu t\u0259min ed\u0259n kafi \u015f\u0259rt tap\u0131lm\u0131\u015fd\u0131r. Misal \u00fcz\u0259rind\u0259 g\u00f6st\u0259rilmi\u015fdir ki, tap\u0131lan \u015f\u0259rt d\u0259qiqdir. Eyni zamanda ba\u015f hiss\u0259 biharmonik operator olan sinqulyar potensiall\u0131 yar\u0131mx\u0259tti elliptik t\u0259nlikl\u0259r sistemin\u0259 bax\u0131lm\u0131\u015fd\u0131r v\u0259 bu sistemin m\u00fcsb\u0259t qlobal h\u0259llinin yoxlu\u011fu \u00fc\u00e7\u00fcn d\u0259qiq qiym\u0259tl\u0259ndirm\u0259 tap\u0131lm\u0131\u015fd\u0131r. Sonra oturaca\u011f\u0131 \u015far\u0131n xarici olan silindird\u0259 zaman arqumentin\u0259 q\u00f6r\u0259 periodik \u0259msall\u0131 yar\u0131mx\u0259tti ikinci t\u0259rtib parabolik t\u0259nlik v\u0259 t\u0259nlikl\u0259r sisteminin m\u00fcsb\u0259t qlobal h\u0259ll\u0259rinin yoxlu\u011fu m\u0259s\u0259l\u0259si \u00f6yr\u0259nilmi\u015f v\u0259 bu halda da h\u0259llin yoxlu\u011fu \u00fc\u00e7\u00fcn d\u0259qiq kafi \u015f\u0259rt tap\u0131lm\u0131\u015fd\u0131r.<\/p>\n