د مقالې اصلي محتوا
خلاصه
اولین‌بار در سال ۱۹۳۳،آبلوزا پایداری هایرز-اولام معادلات دیفرانسیل خطی را بررسی نمود، پس از آن مقالات بسیاری در این زمینه منتشر گردیده است که تعدادی از آن‌ها را می‌توان در مراجع (۱۹،۶) ملاحظه نمود. در این مقاله می‌خواهیم پایداری معادله‌ی دیفرانسیل خطی را در فضای نورم‌دار غیر ارشمیدسی بررسی کنیم. فرض کنیم فضای نورم‌دار غیر ارشمیدسی اعداد حقیقی باشد. معادله دیفرانسیل خطی نا متجانس مرتبه دوم با ضرایب غیر ثابت را در نظر می‌گیریم که در آن توابع داده شده متمادی هستند. در این مقاله پایداری هایرز-اولام این معادله در فضای نورم‌دار غیر ارشمیدسی اعداد حقیقی ثابت می‌کنیم.
کلیدي ټکي
د مقالې جزئیات
د کاپی رایت بیان
د کرییټیو کامنز BY-NC 4.0 نړیوال لایسنسماخذونه
- Czerwik, S. Functional Equations and Inequalities in several variables, (2002). World scientific, Singapore.
- Hyers, D.H., Isac, G. and Rassias, T.M. stability of Functional Equation in Several Variables, (1998). Birkhauser, boston.
- Sahoo. P. K and kannappan, P. Introduction to Functional Equations, (2011). CRC press, boca Raton.
- Obloza, M. Hyers stability of the linear differential equations, (1993). Rocz.nauk. – Dydakt.Pr.Mat .13,259-270.
- Obloza, M. connection between Hyers and Lyapunov stability of the ordinary differential equation, (1997). Rocz.nauk. -Dyadakt.Pr. Mat. 14,141-146.
- Alsina, C and Ger, R. On some inequalities and stability results related to the exponential function, (1998). J.inequal.Appl.2,373-380.
- Gavruta, P, Jung, S-M. and Li, Y. Hyers-Ulem stability for second- order linear differential equation with Electronic. (2011). J. Differ.Equ,.801-805.
- jung, S-M. Hyers –Ulam stability of linear differential equation of first order, (2004). Appl. Math. Lett. 17, 1135-1140.
- Jung, S-M. Hyers –Ulam stability of linear differential equation of first order, II, (2006). Appl. Math. Lett. 19, 854-140.
- Jung, S-M. Hyers. Ulam stability of a system of first order linear differential equation with constant coefficients, (2006). J. Math. Anal. Apple. 320,549-561.
- Miura, T.,Oka ,H,.Talahasi, S-E.and Niwa , N. Hyers –Ulam stability of first order linear differential equation for banach space-valued holomorphic mappings, (2007). J. Math. in equal. 3 ,377-385.
- popa, D. Rasa, I. On the Hyers-Ulam of the linear differential equation, (2011). J. Math. Anal. Appl. 381, 530 537.
- popa, D. Rasa, I. On the Hyers-Ulam of the linear differential operator with non – constant coefficient, (2011). Appl. Math. Compute. 219, 1562- 1568.
- Rus, I, A. Ulam stability of ordinary differential equation, stud. (2009).Univ. Babes-Bolyai, Math.54, 125-134.
- Wang, G.,Zhou, M .and Sun , L. Hyers-Ulam stability of differential. equation of first order, (2008). Appl, Math. Lett. 21, 1024-1028.
- Alqifary, Q.H. and Jung, S-M. On the hyers –Ulam stability of differential equation of second order, (2014). Abstr. Appl. Anal., Article ID 483707.
- Cimpean, D.S. and popa, On the stability of the linear differential equation of higher order with constant coefficient, (2010). Appl. Math. Compute. 217,4141-4146.
- Ghamei, M.B., Gordji, M.E., Alizadeh and B, Park, C. Hyers – Ulam stability of exact second –order linear differential equation, Adv. (2012). Differ. Equ., Article ID 36.
- Li, Y. and shen, Y. Hyers -Ulam stability of linear differential. equation of second order, (2010). Appl. Math. 23, 306-309.
ماخذونه
Czerwik, S. Functional Equations and Inequalities in several variables, (2002). World scientific, Singapore.
Hyers, D.H., Isac, G. and Rassias, T.M. stability of Functional Equation in Several Variables, (1998). Birkhauser, boston.
Sahoo. P. K and kannappan, P. Introduction to Functional Equations, (2011). CRC press, boca Raton.
Obloza, M. Hyers stability of the linear differential equations, (1993). Rocz.nauk. – Dydakt.Pr.Mat .13,259-270.
Obloza, M. connection between Hyers and Lyapunov stability of the ordinary differential equation, (1997). Rocz.nauk. -Dyadakt.Pr. Mat. 14,141-146.
Alsina, C and Ger, R. On some inequalities and stability results related to the exponential function, (1998). J.inequal.Appl.2,373-380.
Gavruta, P, Jung, S-M. and Li, Y. Hyers-Ulem stability for second- order linear differential equation with Electronic. (2011). J. Differ.Equ,.801-805.
jung, S-M. Hyers –Ulam stability of linear differential equation of first order, (2004). Appl. Math. Lett. 17, 1135-1140.
Jung, S-M. Hyers –Ulam stability of linear differential equation of first order, II, (2006). Appl. Math. Lett. 19, 854-140.
Jung, S-M. Hyers. Ulam stability of a system of first order linear differential equation with constant coefficients, (2006). J. Math. Anal. Apple. 320,549-561.
Miura, T.,Oka ,H,.Talahasi, S-E.and Niwa , N. Hyers –Ulam stability of first order linear differential equation for banach space-valued holomorphic mappings, (2007). J. Math. in equal. 3 ,377-385.
popa, D. Rasa, I. On the Hyers-Ulam of the linear differential equation, (2011). J. Math. Anal. Appl. 381, 530 537.
popa, D. Rasa, I. On the Hyers-Ulam of the linear differential operator with non – constant coefficient, (2011). Appl. Math. Compute. 219, 1562- 1568.
Rus, I, A. Ulam stability of ordinary differential equation, stud. (2009).Univ. Babes-Bolyai, Math.54, 125-134.
Wang, G.,Zhou, M .and Sun , L. Hyers-Ulam stability of differential. equation of first order, (2008). Appl, Math. Lett. 21, 1024-1028.
Alqifary, Q.H. and Jung, S-M. On the hyers –Ulam stability of differential equation of second order, (2014). Abstr. Appl. Anal., Article ID 483707.
Cimpean, D.S. and popa, On the stability of the linear differential equation of higher order with constant coefficient, (2010). Appl. Math. Compute. 217,4141-4146.
Ghamei, M.B., Gordji, M.E., Alizadeh and B, Park, C. Hyers – Ulam stability of exact second –order linear differential equation, Adv. (2012). Differ. Equ., Article ID 36.
Li, Y. and shen, Y. Hyers -Ulam stability of linear differential. equation of second order, (2010). Appl. Math. 23, 306-309.