PERIODIC BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS
Abstract
We prove existence results for the solutions of the periodic boundary valueproblem concerning the n-th order functional differential equation with impulses effects and the periodic boundary conditions. Our method is based upon the coincidence degree theory of Mawhin and some technicalinequalities. Examples are presented to illustrate the main results.
Keywords
References
- BAINOV, D.D., et al.; 1989, Periodic boundary value problems foe systems of first order impulsive equations, Differential and Integral Equations, 2(1), 37-43.
- BAINOV, D.D.; SIMEONOV, P.S.; 1993, Impulsive differential equations: periodic solutions and applications, Hacloi: Longman Scientific and Technical.
- CABADA, A.; 1994, The monotone method for first order problems with linear and nonlinear boundary conditions, Applied Mathematics and Computation, 63, 163-186.
- CABADA, A.; NIETO, J. J.; FRANCO, D.; TROFIMCHUK, S. I.; 2000, A generalization of the monotone method for second order periodic boundary value problems with impulses at fixed points, Dynamics of Continuous Discrete and Impulsive Systems, 7, 145-158.
- CHEN, L.; SUN, J.; 2006, Boundary value problems of second order impulsive functional differential equations, Journal of Mathematical Analysis and Applications, 323, 708-720.
- CHU, J.; ZHOU, Z.; 2006, Positive solutions for singular third order periodic boundary value problems, Nonlinear Analysis, 64, 1528-1542.
- CONG, F.; 1998, Periodic solutions for 2kth order ordinary differential equations with nonresonance, Nonlinear Analysis, 32, 787-793.
- CONG, F.; HUANG, Q.; SHI, S.; 2000, existence and Uniqueness of Periodic Solutions for (2n + 1)th-Order Differential Equations, Journal of Mathematical Analysis and Applications, 241, 1-9.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
-
Authors
Yuji Lıu
This is me
Publication Date
December 1, 2007
Submission Date
October 4, 2007
Acceptance Date
October 19, 2007
Published in Issue
Year 2007 Volume: 2 Number: 2