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Uniformly Stable Positive Monotonic Solution of a Nonlocal Cauchy Problem
Faculty of Science, Alexandria University, Alexandria, Egypt
Faculty of Science, Alexandria University, Alexandria, Egypt
Faculty of Science, Garyounis University, Benghazi, Libya
- 1 Faculty of Science, Alexandria University, Alexandria, Egypt
- 2 Faculty of Science, Alexandria University, Alexandria, Egypt
- 3 Faculty of Science, Garyounis University, Benghazi, Libya
Advances in Pure Mathematics·Volume 02 (2012)·Pages 109–113·Published 22 March 2012·DOI10.4236/apm.2012.22015
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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
KeywordsNonlocal Cauchy ProblemLocal and Global Existence Nondecreasing Positive SolutionContinuous DependenceLyapunov Uniformly Stability
- 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
- 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
- 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
- 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.
- 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.
- 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
- 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
- R. F. Curtain and A. J. Pritchard, “Functional Analysis in Modern Applied Mathemat-ics,” Academic Press, New York, 1977.
- 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.
- 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.
- 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.
- 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