Internal nonlocal and integral condition problems of the differential equation \(x' = f(t; x; x')\)


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.


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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


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