KOSHI MASALASI YECHIMI MAVJUDLIGINI PIKAR KETMA-KET YAQINLASHISHLARI USULI ASOSIDA ISBOTLASH
Keywords:
Kalit so‘zlar: Koshi masalasi, oddiy differensial tenglama, Pikar usuli, ketma-ket yaqinlashishlar, mavjudlik teoremasi, Lipshits sharti, integral tenglama.Abstract
Annotatsiya. Mazkur maqolada birinchi tartibli oddiy differensial tenglama uchun qo‘yilgan Koshi masalasining yechimi mavjudligini isbotlash masalasi tahlil qilinadi. Tadqiqotda Koshi masalasi integral tenglamaga keltiriladi va Pikar ketma-ket yaqinlashishlari usuli orqali yechimning mavjudligi asoslanadi. Shuningdek, yechimning berilgan to‘rtburchakli sohada aniqlanishi, funksiyaning uzluksizligi, chegaralanganligi va Lipshits sharti kabi yetarli shartlarning matematik mazmuni ochib beriladi. Maqolada nazariy isbot amaliy misol bilan mustahkamlanib, Lipshits sharti bajarilmagan holatda yechimning yagonaligi buzilishi mumkinligi ham ko‘rsatib o‘tiladi.
References
1. Pontryagin L. S. Oddiy differensial tenglamalar. — Moskva: Nauka, 1982.
2. Coddington E. A., Levinson N. Theory of Ordinary Differential Equations. — New York: McGraw-Hill, 1955.
3. Hartman P. Ordinary Differential Equations. — Philadelphia: SIAM, 2002.
4. Teschl G. Ordinary Differential Equations and Dynamical Systems. — Providence: American Mathematical Society, 2012.
5. Arnold V. I. Ordinary Differential Equations. — Berlin: Springer, 1992.
6. Walter W. Ordinary Differential Equations. — New York: Springer, 1998.
7. Filippov A. F. Differential Equations with Discontinuous Right-Hand Sides. — Dordrecht: Kluwer Academic Publishers, 1988.
8. Hale J. K. Ordinary Differential Equations. — New York: Wiley-Interscience, 1969.
9. Salohiddinov M. S. Oddiy differensial tenglamalar kursi. — Toshkent: O‘zbekiston, 1994.
10. Krasnoselskii M. A., Zabreiko P. P. Geometrical Methods of Nonlinear Analysis. — Berlin: Springer, 1984.
