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Báo cáo hóa học: "Research Article Antiperiodic Boundary Value Problems for Finite Dimensional Differential Systems"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Antiperiodic Boundary Value Problems for Finite Dimensional Differential Systems | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 541435 11 pages doi 10.1155 2009 541435 Research Article Antiperiodic Boundary Value Problems for Finite Dimensional Differential Systems Y. Q. Chen 1 D. O Regan 2 F. L. Wang 1 and S. L. Zhou1 1 Faculty of Applied Mathematics Guangdong University of Technology Guangzhou Guangdong 510006 China 2 Department of Mathematics National University of Ireland Galway Ireland Correspondence should be addressed to D. O Regan donal.oregan@nuigalway.ie Received 16 March 2009 Accepted 28 May 2009 Recommended by Juan J. Nieto We study antiperiodic boundary value problems for semilinear differential and impulsive differential equations in finite dimensional spaces. Several new existence results are obtained. Copyright 2009 Y. Q. Chen et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction The study of antiperiodic solutions for nonlinear evolution equations is closely related to the study of periodic solutions and it was initiated by Okochi 1 . During the past twenty years antiperiodic problems have been extensively studied by many authors see 1-31 and the references therein. For example antiperiodic trigonometric polynomials are important in the study of interpolation problems 32 33 and antiperiodic wavelets are discussed in 34 . Moreover antiperiodic boundary conditions appear in physics in a variety of situations see 35-40 . In Section 2 we consider the antiperiodic problem u f Au t f f u tf t e R E 1.1 ut -u t T t e R where A is an n X n matrix f R X Rn Rn is continuous and f t T x -f t x for all t x e R X Rn. Under certain conditions on the nondiagonal elements of A and f we prove an existence result for E 1.1 . In Section 3 we consider the antiperiodic boundary value problem u f Gu f f t u ty a.e. t e J 0 T t ftk u 0 -u T E