Existence of Solutions of Periodic Boundary Value Problems for Impulsive Functional Duffing Equations at Nonresonance Case. (10th September 2008)

• Record Type: Journal Article
• Authors: Liu, Xingyuan; Liu, Yuji
• Other Names: Zhang Zhitao Academic Editor.
• Is Part Of: Boundary value problems. Volume 2008(2008)
• Publication Date: 2008-09-10
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2008/937138
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : This paper deals with the existence of solutions of the periodic boundary value problem of the impulsive Duffing equations:x ′ ′ ( t ) + α x ′ ( t ) + β x ( t ) = f ( t, x ( t ), x ( α 1 ( t ) ), …, x ( α n ( t ) ) ), a.e. t ∈ [ 0, T ], Δ x ( t k ) = I k ( x ( t k ), x ′ ( t k ) ), k = 1, …, m, Δ x ′ ( t k ) = J k ( x ( t k ), x ′ ( t k ) ), k = 1, …, m, x ( i ) ( 0 ) = x ( i ) ( T ), i = 0, 1 . Sufficient conditions are established for the existence of at least one solution of above-mentioned boundary value problem. Our method is based upon Schaeffer's fixed-point theorem. Examples are presented to illustrate the efficiency of the obtained results.