BIRINCHI TARTIBLI DIFFERENSIAL TENGLAMALARNING YECHIMLARINI TOPISHDA PEANO MAVJUDLIK TEOREMASINING AHAMIYATI
Authors/Creators
- 1. Termiz davlat pedagogika instituti magistranti
Description
Ushbu maqolada birinchi tartibli differensial tenglamalar nazariyasida Peano mavjudlik teoremasi va uning matematikadagi tutgan o'rni batafsil tahlil etilgan. Peano teoremasi Koshi masalasining yechimi mavjudligini kafolatlash uchun zarur va yetarli shartlarni belgilaydi. Maqolada teoremaning to'liq sharti va isboti, uning Pikar-Lindelöf teoremasi bilan qiyosiy tahlili, hamda amaliy jihatlari ko'rib chiqilgan. Shuningdek, yechimning global mavjudligi, maksimal yechim tushunchasi va yechimning yo'qolishi hodisalari tadqiq qilingan. Teoremaning o'ziga xos xususiyatlari — Lipshits sharti talab qilinmasligidan kelib chiqadigan afzalliklar va kamchiliklar — ham muhokama qilingan. Olingan natijalar differensial tenglamalar nazariyasining asosiy tamoyillarini yanada chuqur tushunishga xizmat qiladi.
Files
64-68.pdf
Files
(229.9 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:d91f220e425ea87d09e3b78513f48893
|
229.9 kB | Preview Download |
Additional details
References
- 1. Peano, G. (1886). Sull'integrabilità delle equazioni differenziali di primo ordine. Atti della Reale Accademia delle Scienze di Torino, 21, 677–685.
- 2. Coddington, E. A., & Levinson, N. (1955). Theory of Ordinary Differential Equations. McGraw-Hill, New York.
- 3. Hartman, P. (2002). Ordinary Differential Equations (2nd ed.). Society for Industrial and Applied Mathematics (SIAM), Philadelphia.
- 4. Teschl, G. (2012). Ordinary Differential Equations and Dynamical Systems. American Mathematical Society, Providence, RI.
- 5. Filippov, A. F. (1988). Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers, Dordrecht.