Internal nonlocal and integral condition problems of the differential equation \(x' = f(t; x; x')\)
-
1669
Downloads
-
2728
Views
Authors
A. M. A. El-Sayed
- Department of Mathematics, Alexandria University, Alexandria, Egypt.
E. M. Hamdallah
- Department of Mathematics, Alexandria University, Alexandria, Egypt.
KH. W. Elkadeky
- Department of Mathematics, Faculty of Science, Garyounis University, Beng- hazi, Libya.
Abstract
In this work, we are concerned with the existence of at least
one absolutely continuous solution of the Cauchy problem for the differential
equation \(x' = f(t; x; x'), t \in (0; 1)\) with the internal nonlocal condition m
\(\sum^m_{k=1} a_kx(\tau_k) = x_o, \tau_k \in (c, d) \subseteq (0; 1)\). The problem of the integral
condition
\(\int^d_c x(s) dg(s) = x_o\) will be considered.
Share and Cite
ISRP Style
A. M. A. El-Sayed, E. M. Hamdallah, KH. W. Elkadeky, Internal nonlocal and integral condition problems of the differential equation \(x' = f(t; x; x')\), Journal of Nonlinear Sciences and Applications, 4 (2011), no. 3, 193--199
AMA Style
El-Sayed A. M. A., Hamdallah E. M., Elkadeky KH. W., Internal nonlocal and integral condition problems of the differential equation \(x' = f(t; x; x')\). J. Nonlinear Sci. Appl. (2011); 4(3):193--199
Chicago/Turabian Style
El-Sayed, A. M. A., Hamdallah , E. M., Elkadeky, KH. W.. "Internal nonlocal and integral condition problems of the differential equation \(x' = f(t; x; x')\)." Journal of Nonlinear Sciences and Applications, 4, no. 3 (2011): 193--199
Keywords
- Nonlocal conditions
- integral condition
- existence of solution
- fixedpoint theorem
MSC
References
-
[1]
M. Benchohra, E. P. Gatsori, S. K. Ntouyas, Existence results for seme-linear integrodifferential inclusions with nonlocal conditions , Rocky Mountain J. Mat. , Vol. 34, No. 3 (2004)
-
[2]
M. Benchohra, S. Hamani, S. Ntouyas, Boundary value problems for differential equations with fractional order and nonlocal conditions, Nonlinear Analysis , 71 (2009), 2391-2396.
-
[3]
A. Boucherif , First-order differential inclusions with nonlocal initial conditions, Applied Mathematics Letters , 15 (2002), 409-414.
-
[4]
A. Boucherif, Nonlocal Cauchy problems for first-order multivalued differential equations, Electronic Journal of Differential Equations , 2002 (2002), 1-9.
-
[5]
A. Boucherif, R. Precup, On The nonlocal Initial Value Problem for First Order Differential Equations, Fixed Point Theory, 4 (2003), 205-212.
-
[6]
A. Boucherif, Semilinear evolution inclusions with nonlocal conditions, Applied Mathematics Letters , 22 (2009), 1145-1149.
-
[7]
R. F. Curtain, A. J. Pritchard , Functional Analysis in modern, Applied Mathematics Academic Press , (1977)
-
[8]
J. Dugundji, A. Grans , Fixed Point Theory, Monografie Mathematyczne, PWN, Warsaw (1963)
-
[9]
A. M. A. El-Sayed, Sh. A. Abd El-Salam, On the stability of a fractional order differential equation with nonlocal initial condtion, EJQTDE, 29 (2008), 1-8.
-
[10]
A. M. A. El-Sayed, Kh. W. Elkadeky , Caratheodory theorem for a nonlocal problem of the differential equation x' = f(t; x' ), Alexandria j. of Math., Vol. 1 No. 2 (2010)
-
[11]
E. Gatsori, S. K. Ntouyas, Y. G. Sficas, On a nonlocal cauchy problem for differential inclusions, Abstract and Applied Analysis , (2004), 425-434.
-
[12]
K. Goebel, W. A. Kirk , Topics in Metric Fixed point theory, Cambridge University press, Cambridge (1990)
-
[13]
G. M. Guerekata , A Cauchy problem for some fractional abstract differential equation with non local conditions, Nonlinear Analysis , 70 (2009), 1873-1876.
-
[14]
H. Liu, D. Jiang , Two-point boundary value problem for first order implicit differential equations, Hiroshima Math.J., 30 (2000), 21-27.
-
[15]
R. Ma, Existence and Uniqueness of Solutions to First - Order Three - Point Boundary Value Problems, Applied Mathematics Letters, 15 (2002), 211-216.