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Biz ikki o‘lchamli panjarada Hvμ-  bir zarrachali diskret Schrödinger operatorini o‘rganamiz. Hvμ  operatorning muhim spektrdan yuqorida xos qiymatlari mavjudligi yoki mavjud emasligini va sonini aniqlaymiz. Bundan tashqari, xos qiymat funksiyasining xossalarini  va yetarlicha kichik, musbat μ larda xos qiymatning asimptotikasini o‘rganamiz

  • Ўқишлар сони 0
  • Нашр санаси 12-08-2024
  • Мақола тилиO'zbek
  • Саҳифалар сони131-139
Ўзбек

Biz ikki o‘lchamli panjarada Hvμ-  bir zarrachali diskret Schrödinger operatorini o‘rganamiz. Hvμ  operatorning muhim spektrdan yuqorida xos qiymatlari mavjudligi yoki mavjud emasligini va sonini aniqlaymiz. Bundan tashqari, xos qiymat funksiyasining xossalarini  va yetarlicha kichik, musbat μ larda xos qiymatning asimptotikasini o‘rganamiz

Русский

Мы исследуем одночастичный дискретный оператор ШредингераHvμна одномерной решетке T2. Установим существование или несуществование, а также конечность собственных значений оператора Hvμ лежащих ниже существенного спектра. Кроме того, мы изучаем свойства собственных значений в зависимости от μ, в частности, находим асимптотику собственных значений при достаточно малом и положительном μ

English

We consider the family Hvμ of discrete Schrödinger-type operator in two-dimensional lattice T2. We establish the existence or non-existence and also the finiteness of eigenvalues of Hvμ lying above the essential spectrum. Moreover, we study the properties of eigenvalues as a function of μ, in particular, we find the asymptotics of eigenvalues as sufficiently small and positive μ.

№ Муаллифнинг исми Лавозими Ташкилот номи
1 Almuratov F.M. dotsent Miliy unversiteti Jizzax filyali
2 Pardabaev M.. dotsent O'zbekiston Finlandiya pedagogika instituti
3 Bobonazarova A.. Magistr Milliy unversitet Jizzax filyali
№ Ҳавола номи
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5 [5] A. Khalkhuzhaev, Sh.Kholmatov, M.Pardabaev: Expansion of eigenvalues of the perturbed discrete bilaplacian. Journals Monatshefte fur Mathematik, (2022)
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8 [8] Shokhrukh Yu. Kholmatov, Saidakhmat N. Lakaev, Firdavsjon M. Almuratov: On the spectrum of Schrödinger-type operators on two dimensional lattices, Journal of Mathematical Analysis and Applications, 514(2) (2022), 126363. https://doi.org/10.1016/j.jmaa.2022.126363
9 [9] Lakaev, S.N., Boltaev, A.T. & Almuratov, F.M. On The Discrete Spectra of Schrödinger-Type Operators on one Dimensional Lattices. Lobachevskii J Math 43, 770–783 (2022).https://doi.org/10.1134/S199508022206018X
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