Criteria for the uniqueness of a solution for some differential-operator equation

Baltabek  Kanguzhin; Bakytbek Koshanov

doi:10.70474/2pmhkg48

Авторлар

Балтабек Есматұлы Қанғожин Al-Farabi Kazakh National University Author https://orcid.org/0000-0001-5504-6362
Бақытбек Дәнебекұлы Қошанов Математика және математикалық модельдеу институты Author https://orcid.org/0000-0002-0784-5183

DOI:

https://doi.org/10.70474/2pmhkg48

Кілт сөздер:

азғындалмаған шекаралық шарттар, оператордың меншікті мәндері, оператордың спектрі, симметриялы операторлар, толық ортогональды жүйелер, шешімнің бірегейлігі, Штурм-Лиувилл теңдеуі

Аңдатпа

Бұл мақалада екі коммутацияланатын A және B операторлардың айырымы түрінде берілген шекаралық есепке сәйкес келетін симметриялы L операторы қарастырылады. Егер A операторының спектрі B операторының спектрімен қиылыспайтын болса және B операторының анықталу облысы азғындалмаған шекаралық шарттармен берілсе, онда Lu = (B–A)u = 0 операторлық теңдеу шешімінің бірегейлігіне кепілдік беріледі. Бұл жұмыста тұжырымдалған шекаралық есептің бірегейлік критерийі қолданыстағы еңбектердің нәтижелерінен айырмашылығы B операторының түбірлік функциялар жүйесі сәйкес кеңістікте базис құрмаған кезде де қанағаттандырылады. Бұл ретте A сызықты операторының тұйықтығы ғана қажет.

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