Geodesic
Internal nonlocal and integral condition problems of the differential equation $x' = f(t; x; x')$
El-Sayed, A. M. A.1 ; Hamdallah , E. M. 1 ; Elkadeky, KH. W.2
1 Department of Mathematics, Alexandria University, Alexandria, Egypt
2 Department of Mathematics, Faculty of Science, Garyounis University, Beng- hazi, Libya
Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 3, p. 193-199.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.004.03.02
Classification : 26A33, 34A12, 34A40
Keywords: Nonlocal conditions, integral condition, existence of solution, fixedpoint theorem

El-Sayed, A. M. A. 1 ; Hamdallah , E. M.  1 ; Elkadeky, KH. W. 2

1 Department of Mathematics, Alexandria University, Alexandria, Egypt
2 Department of Mathematics, Faculty of Science, Garyounis University, Beng- hazi, Libya 
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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 its applications, Tome 4 (2011) no. 3, p. 193-199. doi : 10.22436/jnsa.004.03.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.03.02/

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