APM  Vol.2 No.2 , March 2012
Uniformly Stable Positive Monotonic Solution of a Nonlocal Cauchy Problem
ABSTRACT
In this paper, we study the existence of a uniformly stable positive monotonic solution for the nonlocal Cauchy problem with the nonlocal condition where

Cite this paper
A. El-Sayed, E. Hamdallah and K. Elkadeky, "Uniformly Stable Positive Monotonic Solution of a Nonlocal Cauchy Problem," Advances in Pure Mathematics, Vol. 2 No. 2, 2012, pp. 109-113. doi: 10.4236/apm.2012.22015.
References
[1]   B. Ahmad and J. J. Nieto, “Existence of Solution for Non- local Boundary Value Problems of Higher-Order Nonlin- ear Frac-tional Differential Equations,” Abstract and Applied Analysis, Vol. 2009, 2009, pp. 1-9. doi:10.1155/2009/494720

[2]   M. Benchohra, J. J. Nieto and A. Ouahab, “Second-Order Boundary Value Problem with Integral Boundary Conditions,” Boundary Value Problems, Vol. 2011, 2011, pp. 1-9. doi:10.1155/2011/260309

[3]   A. Boucherif, “First-Order Differential Inclusions with Nonlocal Initial Conditions,” Applied Mathematics Letters, Vol. 15, No. 4, 2002, pp. 409-414. doi:10.1016/S0893-9659(01)00151-3

[4]   A. Boucherif, “Nonlocal Cauchy Problems for First-Order Multivalued Dif-ferential Equations,” Electronic Journal of Differential Equations, Vol. 2002, No. 47, 2002, pp. 1-9.

[5]   A. Boucherif and R. Precup, “On The Nonlocal Initial Value Problem for First Order Differential Equations,” Fixed Point Theory, Vol. 4, No 2, 2003, pp. 205-212.

[6]   M. Benchohra, E. P. Gatsori and S. K. Ntouyas, “Existence Results for Seme-Linear Integrodif-ferential Inclusions with Nonlocal Conditions,” Rocky Mountain Journal of Mathematics, Vol. 34, No. 3, 2004, pp. 833-848. doi:10.1216/rmjm/1181069830

[7]   Y. K. Chang and J. J. Nieto, “Existence of Solutions for Impulsive Neutral Inte-gro-Differential Inclsions with Non- local Initial Conditions via Fractional Operators, Numerical Functional Analysis and Optimization, Vol. 30, No. 3- 4, 2009, pp. 227-244. doi:10.1080/01630560902841146

[8]   R. F. Curtain and A. J. Pritchard, “Functional Analysis in Modern Applied Mathemat-ics,” Academic Press, New York, 1977.

[9]   A. M. A. El-Sayed and Sh. A. Abd El-Salam, “On the Stability of a Fractional-Order Differential Equation with Nonlocal Initial Condi-tin,” Electronic Journal of Differential Equations, Vol. 2009, No. 29, 2008, pp. 1-8.

[10]   A. M. A. El-Sayed and Kh. W. Elkadeky, “Caratheodory Theorem for a Nonlocal Problem of the Differential Equation ,” Alexandria Journal of Mathematics, Vol. 1, No. 2, 2010, pp. 8-14.

[11]   A. M. A. El-Sayed and Kh. W. Elkadeky, “Solutions of a Class of Nonlocal Problems for the Differential Inclusion,” Applied Mathematics and Information Sciences, Vol. 5, No. 2, 2011, pp. 413-421.

[12]   A. M. A. El-Sayed, E. M. Hamdallah and Kh. W. Elkadeky, “Solutions of a Class of Deviated-Advanced Non- local Problem for the Dif-ferential Inclusion ,” Abstract and Applied Analysis, Vol. 2011, 2011, pp. 1-9. doi:10.1155/2011/476392

[13]   E. Gatsoi, S. K. Ntouyas and Y. G. Sficas, “On a Nonlocal Cauchy Problem for Differential Inclusions,” Abstract and Applied Analysis, Vol. 2004, 2004, pp. 425-434. doi:10.1155/S108533750430610X

[14]   K. Goebel and W. A. Kirk, “Topics in Metric Fixed Point Theory,” Cambridge University Press, Cambridge, 1990. doi:10.1017/CBO9780511526152

[15]   A. Lasota and Z. Opial, “An Application of the Kakutani-Ky-Fan Theorem in the Theory of Ordinary Differential Equations,” Bull. Acad. Polon. Sci. Ser. Sci. Math. Astoronom. Phys, Vol. 13, 1955, pp. 781-786.

[16]   R. Ma, “Existence and Uniqueness of Solutions to First- Order Three-Point Boundary Value Problems,” Applied Mathematics Letters, Vol. 15, No. 2 2002, pp. 211-216. doi:10.1016/S0893-9659(01)00120-3

[17]   S. K. Ntouyas, “Nonlocal Initial and Boundary Value Problems: A Survey,” In: A. Canada, P. Drabek and A. Fonda, Eds., Hand Book of Dif-ferential Equations, Vol. II Elsevier, New York, 2005.

[18]   A. Vlez-Santiago, “Quasi-Linear Boundary Value Problems with Generalized Nonlocal Boundary Conditions, Nonlinear Analysis,” Theory, Methods and Applications, Vol. 74, 2011, pp. 4601-4621. doi:10.1016/j.na.2011.03.064

 
 
Top