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Báo cáo hóa học: "Research Article The Solution of Two-Point Boundary Value Problem of a Class of Duffing-Type Systems with Non-C1 Perturbation Term"

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 The Solution of Two-Point Boundary Value Problem of a Class of Duffing-Type Systems with Non-C1 Perturbation Term | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 287834 12 pages doi 10.1155 2009 287834 Research Article The Solution of Two-Point Boundary Value Problem of a Class of Duffing-Type Systems with Non-C1 Perturbation Term Jiang Zhengxian and Huang Wenhua School of Sciences Jiangnan University 1800 Lihu Dadao Wuxi Jiangsu 214122 China Correspondence should be addressed to Huang Wenhua hpjiangyue@163.com Received 14 June 2009 Accepted 10 August 2009 Recommended by Veli Shakhmurov This paper deals with a two-point boundary value problem of a class of Duffing-type systems with non-C1 perturbation term. Several existence and uniqueness theorems were presented. Copyright 2009 J. Zhengxian and H. Wenhua. 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 Minimax theorems are one of powerful tools for investigation on the solution of differential equations and differential systems. The investigation on the solution of differential equations and differential systems with non-C1 perturbation term using minimax theorems came into being in the paper of Stepan A.Tersian in 1986 1 . Tersian proved that the equation Lu t f t u jf L - d2 dt2 exists exactly one generalized solution under the operators Bj j 1 2 related to the perturbation term f t u f being selfadjoint and commuting with the operator L - d2 dt2 and some other conditions in 1 . Huang Wenhua extended Tersian s theorems in 1 in 2005 and 2006 respectively and studied the existence and uniqueness of solutions of some differential equations and differential systems with non-C1 perturbation term 2-4 the conditions attached to the non-C1 perturbation term are that the operator B ù related to the term is self-adjoint and commutes with the operator A where A is a selfadjoint operator in the equation Au f t u . Recently by .